Very generically, if the options were granted when you were non-resident in the UK and had nothing to do with your future UK duties, then you won't be taxed in the UK on the ordinary income element (i.e. difference between grant and vest price). You would be taxed in the US though -- again at ordinary income rates from the grant to vest price.
Now that you are resident in the UK, if you continue to hold the shares after exercise, you may generate a capital gain on the difference between vest price and the ultimate sales price. The US would look to charge a similar capital gain. However, if you are charged the capital gain in the UK, you would get credit on your US return.
As for accountants/financial advisors -- what is your price range?