If you've been prudent over the years you will have saved some money into a ROTH IRA. This is a US retirement account and one of the best ways for a regular US/UK person to invest in mutual funds because it has tax advantages and the retirement wrapper shelters it from the complications of owning cross border pooled investments.
As long as you have enough US earned income and your Modified Adjusted Gross Income is below some upper limit set by the IRS ($120k this year) you can contribute to a ROTH. You put money in that you've already paid tax on and it will grow inside the ROTH US tax free and distributions will be US tax free too.
So now what happens if you are a US citizen living in the UK. Well under the UK/US tax treaty ROTH growth and distributions are also UK tax free, the Technical Explanation of Article 17 para 1 puts it surprisingly plainly:
"However, the State of residence, under subparagraph (b), must exempt from tax any amount of such pensions or other similar remuneration that would be exempt from tax in the State in which the pension scheme is established if the recipient were a resident of that State. Thus, for example, a distribution from a U.S. "Roth IRA" to a U.K. resident would be exempt from tax in the United Kingdom to the same extent the distribution would be exempt from tax in the United States if it were distributed to a U.S. resident. The same is true with respect to distributions from a traditional IRA to the extent that the distribution represents a return of non-deductible contributions. Similarly, if the distribution were not subject to tax when it was “rolled over” into another U.S. IRA (but not, for example, to a U.K. pension scheme), then the distribution would be exempt from tax in the United Kingdom."
and Article 18 para 1 allows for tax free growth inside a pension wrapper until distributions are made.
So if you are a US citizen residing in the UK how do you contribute to a ROTH. All you have to do is have enough earned income on your 1040. To do that you use the Foreign Earned Income Exclusion carefully and only exclude a portion of your UK earned income leaving enough so you can qualify to make ROTH contributions, but after subtraction of your exemptions and deductions you have no US taxable income. However, any income you exclude must be added back to determine your MAGI limits for your ROTH contribution.
http://www.irs.gov/businesses/small/international/article/0,,id=97137,00.htmlOr you don't use the FEIE at all and use foreign tax credits and your exemptions and deductions to cover your US tax bill.