You should contact a tax adviser licensed in the US who is familiar with the US-UK tax treaty. Two major firms dealing with this in the UK are British American Tax and American Tax Returns. There are many others, and technically any US-licensed CPA or EA can give you an advice on the issue, but do check for the relevant experiences.
That said... Generally the answer is yes, you'll pay taxes in both countries. The US allows foreign tax credit on the amounts attributable to foreign income, however many times the credit doesn't cover the actual tax paid (because of the way it is calculated).
I'm not familiar with the US-UK tax treaty, but many other treaties include a provision that if you're sent by your US employer to the other country for a temporary assignment (usually up to 6 months), the other country will not tax you. Check if the UK treaty has such a provision. If it doesn't - then you'll pay UK taxes.