I can't run for President (unless the Schwarzenegger amendment gets passed!

) so I'll think in terms of Prime Minister over here.
Constitution1. Immediate abolition of the hereditary monarchy, to be replaced in all duties and privileges, but not in powers, with an elected monarch. Qualification for candidacy would be dependent on never having been a member of a political party (immediately putting paid to the "President Blair/Thatcher" nightmare scenario bandied about by monarchists).
2. Crown prerogative to disappear altogether - the central place of the monarch in the British constitution to be replaced by "the people", including in oaths of office for politicians, police officers, the military, etc. The "People's Prerogative", particularly with regard to patronage, would reside not with the executive but with the legislature.
3. Abolish the House of Lords and replace it with issue-specific committees for each legislative bill, selected randomly from the electoral roll like a jury.
4. Disestablishment of the Church, with the new constitution to be expressly and resolutely secular. All churches either become registered charities, in which case their good works become subject to independent scrutiny to make sure their tax exempt status is valid, or private businesses, to be taxed as such.
Tax1. Taxes on fuel, alcohol, tobacco, etc to be frozen at current levels linked to inflation. Companies in these sectors would then be visible when they use the tax regime as cover for the price gouging they consistently indulge in.
2. Inheritance tax threshold to be raised to half a million pounds, but the rate to be raised to 50%. Rates to rise to 100% for any "dynasitc" wealth or income inherited - i.e anything (other than physical property that the beneficiaries intend to live in or use themselves, rather than sell, rent or lease) that was itself bequeathed to the testator from a previous generation. Meritocratic social mobility requires downward as well as upward movement, and inherited dynastic wealth is as much a barrier to social and economic mobility as those imposed by poverty.
3. Personal income tax allowances to be increased to £10,000 for each individual.
4. Basic income tax rate rises to 25%, to threshold of £40,000 (i.e. you can earn £50,000, and pay £10,000 tax on it, so the effective rate is 20%)
5. Intermediate income tax rate of 50% to threshold of £90k (i.e. the first £10 is tax free, the next £40k pays £10k, and the next £50k pays £25k. So if your gross earnings are £100k, you pay £35k tax, or 35%)
6. Top tax rate of 70% on gross earnings above £100k. Quit whining, you're still rich.
7. Tax threshold levels to be linked to average earnings and automatically to rise with them at the start of each tax year, so the split of tax taken from each band always stays the same (until the other guy comes in and ruins everything).
8. Benefits in kind, and capital gains, to be taxed in exactly the same way under the same regime, based on the higher of the two values - that spent by the donor or that gained by the receiver - but always paid by the recipient. If your share option scheme makes you a millionaire when your normal salary is £40k, you get taxed like a millionaire.
9. No other personal allowances or deductables.
10. Special nightclasses to be instituted to retrain all the accountants who lose their jobs because the income tax system is now simple enough for everyone to understand.
11. Flat rate purchase tax of 10% on everything.
12. Abolish Council Tax and use local incomes taxes instead, based on the central system outlined above, with only the rates being variable, not the thresholds. No central government component - let's make the system transparent. The central savings should help pay for taking the lowest earners out of the income tax system altogether.
13. Abolish employers payroll taxes (i.e. employers NI contributions) but shift corporation tax to a turnover basis. It should mirror personal taxation entirely - small businesses should pay no tax at all, bigger ones should pay intermediate amounts, and big ones should pay more, and the definitions of small, bigger and big should be set in stone.
14. This turnover tax should be set low and the thresholds high - maybe 0.3% at the lower level, perhaps 0.5%-1% at the top - but should apply to all revenues generated on UK operations. If you want to trade here, you pay the going rate of tax here (Messrs Murdoch, Fayed, Branson, etc., please note).
15. No import or export taxes on any good or service. If it gets used or applied inside the UK, it gets taxed at the going rate. If it doesn't, it doesn't pay tax while it sits in storage here.
Domestic policy1. Institute a qualification system -
a la Green Card - for British residency for non-EU citizens, and deport people found to be here that don't qualify. But reemphasise asylum policy, to get people away from the idea that refugees and illegal immigrants are the same thing.
1 a. In addition, all British citizens resident abroad, are liable to income tax on all income derived abroad, on penalty of forfeiture of their citizenship. No more whining tax exiles in tax havens - you're either British, or you're not, and British people pay British taxes (Messrs Connery, Caine, If you don't like it, get citizenship somewhere else.
1 b. As part of this, there would be a concerted campaign of negotiations to repatriate some or all of the taxes raised in this way to the country of residence, in return for collecting the taxes on Britain's behalf). If the local rate is 5% and the ex-pat pays 50% tax, then 5% is refunded locally, and 45% comes back to Britain. The host country still gets what they are entitled to, and the Brit still pays for the privilege of carrying one of the world's most respected passports. No sense punishing the locals, and no great loss to the Brit, who is only paying what they would have at home, with (chances are) much better weather.
2. Scrap PFI/PPP going forward, and only use private tenders for public works where public works have been tried and failed. This applies to hospital cleaners as well and hospital builders.
3. Increase military spending, particularly on the Royal Navy and Air Force, with the medium term aim of having forces deployable on their own, with no US support. This would involve a shift away from the GPS network to something else, but that's no bad thing, and defence procurement policies that didn't first ask "will it be compatible with what are the Americans using?"
4. Stop going down the cul-de-sac of "choice" as a way to improve public services. People don't want to have to choose a school for their kids or a hospital for their sick mother. They want the local one to be good.
5. Scrap the 50% target of people to have first degree qualifications. It's too high. Go back to something sensible, achievable and affordable like 10-15%, and fund it publicly. Use any cost savings, plus additional public money, to restart the emphasis on work apprenticeships to produce a vocationally skilled workforce.
6. Restructure the police force, with some additional investment as necessary, to produce more beat policemen and, more particularly, an expanded detective branch. Prison is not a deterrant to crime when criminals think they will not be caught. So catch more of them.
International affairs1. Voluntary revocation of Britain's permanent UNSC seat in return for an EU, Indian, Japanese - the world doesn't need us there any more. This would be conditional on France giving up theirs too. Also, move to qualified majority votes, rather than vetos, in all UNSC decisions.
2. Scrapping of all manufacturing and agricultural subsidies within the EU, and tariffs between the EU and other countries; the spending saved to be diverted to other programs, such as
a. environmental protection
b. subsidisation of leisure and tourism. Make flying to Europe as cheap for Americans as driving to the mall

, and more attractive than the theme park belts of Florida or LA. Not entirely stupid, since you'll be spending your money once you get here.
c. basic and applied scientific research, especially into areas such as cloning therapies, particle physics, and possible replacements for the internal combustion engine. Any patents that result to be 50% owned by the inventor and 50% by the EU, so the public domain benefits directly from its investment.
3. Intelligence services to be directed by the apolitical head of state, not the political government of the day. No more directed collection of intelligence to suit political objectives - political policy decisions instead to be taken after consideration of independently gathered intelligence.
4. Shift emphasis of foreign embassies abroad from being the promotional arm of UK Ltd to being more about protecting and supporting British citizensand their interests, whether at home or abroad.
5. Concerted pressure in every global trade and diplomatic forum to tax aviation fuel at the going rate in every tax jurisdiction on the planet. No transportation market can be a level playing field while aviation gets such a hidden subsidy.