GMT is very nearly the same thing as UTC. Think of it as a reference rather than timezone, but one that happens to be used by a few places half the time.

It's just easier to think of yourself in UTC/GMT all the time (known as Zulu time or /Z in the aviation world) and deal with the relative offsets later. Don't forget that US Daylight Saving has different start/end dates to the UK while you're at it too...