The majority of US citizens who are resident in the UK are not domiciled within the UK. Consequently they can invest outside of the UK and pay no UK tax on interest, dividends, capital gains etc providing that the investment income is not brought to the UK.
This is a standard tax planning technique, which I frequently advise on in my day to day existence.
For longer-term savings there are several classes of assets available, including stocks, bonds, commodoties, real estate, precious metals, cash, insurance policies and other collective investments.
Depending on family size, nationalities, personal expectations etc the correct investment will differ in each case. Investment advice in the UK can only be given by an Independent Financial Adviser (IFA) authorised by the Financial Services Authority (FSA). An FSA registered adviser will him/herself want to protect his/her liability by ensuring that advice given will not cause any adverse tax effects. The first place to start seeking investment advice has, therefore, got to be an IFA.
Several UK investments are not available to US citizens or residents because of SEC regulation. Others would be foolish to choose because of the tax consequences (either UK or US).
I note that nun already has appointed a personal tax adviser so will be able to get full tax advice from that person since s/he will have full knowledge of nun's circumstances. If any further explanation would assist others, please shout! No question is stupid!