(Popping in...)
The US doesn't recognise dual citizenship and will remove citizenship if you pledge alliegance to another state.
Not necessarily true, Fiona. The U.S. doesn't formally recognize dual citizenship, but hasn't taken any actions to prohibit it. The only way you can lose your U.S. citizenship is by affirmative actions showing intent:
The loss of U.S. citizenship can only occur if a person's actions demonstrate an intent to give up his or her citizenship. Such actions might include:
Serving in the armed forces of a country which is engaged in hostilities against the United States.
Formally renouncing one's U.S. citizenship in front of a duly authorized U.S. official.
Committing an act of treason against the United States, or attempting or conspiring to overthrow the U.S. Government.
Voluntarily applying for another citizenship will only terminate your U.S. citizenship if you have the intention of terminating it. [link]
Jars, it shouldn't be a problem for your DH to obtain UK citizenship and keep his U.S. A high school friend of mine lives in London, is married to a Scotsman, and is going for UK citizenship. He is not losing his U.S. passport.