And I am assuming that you have an unlocked phone that will work in the UK ? If not, then it might be better to buy a phone and a SIM. Having said that getting a phone unlocked over here is easier than in the USA in my experience so it may not be necessary to buy a phone.

If your phone is dual band, it will normally work at either 1800MHz or 900MHz.
If it is tri-band, it will work at 1800MHz, 900MHz or 1900MHz.
A quad-band phone should work at 1800MHz, 900MHz, 1900MHz or 850MHz.
If it is CDMA it will not work here.