How Long Does It Take For A Letter To Get From The UK To The US?

3-8 days, depending mostly on where you are sending it to.

3 days to a big hub like New York City or Boston.
4 days to most other places on the East Coast.
4 days to a hub place in the midwest, like Chicago.
5-6 days to most places in the midwest.
5 days or so to a big place on the West Coast (LA, San Fran).
About 6 days to a secondary place on West Coast (San Diego, Portland, Seattle).
6-7 days to most of the West Coast.

Another 2 days or so to get to Alaska or Hawaii.

That all applies most of the year, for items sent by airmail.  If you're sending stuff between about 15-25 November, the times speed up (by 1-3 days).  But then from about 25 November until early January, they double or worse (so, 12 or more days to get to San Diego).

Small packet rate is a bit slower.  Items sent by surface mail can take anywhere between 10 days and 10 weeks to arrive, although 5-6 weeks is pretty typical.