Global Entry Procedures and Timelines of Applications and Renewals for UK citizens
I can confirm Global Entry is available to certain UK passport holders, by certain I mean its currently being trialled. You can only join if you are invited by Virgin / British Airways and you have to be one of their frequent flyers (highest tier) when filling in your application you need a promotional code which the airlines will give you if you qualify and of course you need to complete a CRB check.
I completed the process earlier this year and was approved, it goes without saying I actually enjoy flying into JFK now as opposed to being custom to waiting in line for a few hours!
The application process took 12 weeks for me though this was just before the summer holidays and expected due to an increase in registration!
Hope this helps.