I suppose I should introduce myself here.
I am a US tax accountant specializing in Americans living abroad, particularly in Britain, but also worldwide.
Stateside accountants will be unfamiliar with UK tax laws, so they won't be able to give advice as to how to best structure your your investments and payroll for the lowest income, inheritance, and capital gains taxes between both countries.
My fees are far higher than what you're probably used to if you've just moved from the US, but I recommend that people who can't afford quality work split the work into advice and preparation. If you buy the advice from a dual taxation specialist, and the preparation from two persons, a US preparer in the states and a UK preparer here in the UK, you can get the same high quality a lower overall cost.
I would say that if you're worried about missing something, it's best to see an accountant that uses a tax programme, not one that does returns by hand (they're still out there!). The maths for overseas tax returns can be extremely complicated, and you shouldn't be paying someone to run those kinds of sums by hand for you.
I also provide referrals to US lawyers and US and UK accountants.