well everyone sez the jailbreak is for much more than free apps, but for me its the apps lol! yeah you could just find out the carrier and switch to that and problem solved. if the seller sells lots of phone i doubt he keeps records of what networks the phones are on. sim cards are free why not strike now and go onto all the uk network websites and order a free sim so your covered for worst case scenario where you have to physically test each sim.
The imei unlock is done remotley so once you find out what network its on all you have to do is phone them. no need to take it to a store as they will just take your order like a call center agent will. like i said it will probably take them a week or two to process your unlock order.