Unfortunately, you cannot use a Verizon iPhone in the UK - it would have to be the AT&T version. That said, even with an AT&T version, you need AT&T to factory unlock the phone. AT&T has a policy against doing this, so it is nearly impossible.
If you just take it to "some guy" then he will be doing an after-market or out-of-factory unlock, which means that it will lose the capability to access 3G networks unless it is on the original network to which it was locked...
For example, if I had an AT&T iPhone and went to "some guy" in the UK, he could unlock the phone to work on any carrier. Then I could get a SIM from any carrier like T-Mobile, Three or O2. When I put that UK SIM into the phone, I would not be able to access 3G speeds on internet, which would be painstakingly slow.
The best option here is to sell your phone in the USA for cash. When you get to the UK, sign up for a contract such as the T-Mobile Full Monty plan where you get an iPhone 4 for free, or iPhone 4S for cheap. When you sign up for the contract with T-Mobile (or whatever provider) tell them you need the phone unlocked so that you can use it on travel to the USA. They will FACTORY UNLOCK the phone for you on the spot and then you will be able to use the phone in the USA with 3G, using a pay-as-you-go/monthly SIM when you visit.
Full Monty Plan from T-Mobile UKhttp://www.t-mobile.co.uk/shop/pay-monthly/lg-prada/the-full-monty-36-24m/extras/ [nofollow] T-Mobile USA Month SIM Optionshttp://prepaid-phones.t-mobile.com/monthly-4g-plans [nofollow] T-Mobile USA Daily SIM Optionshttp://prepaid-phones.t-mobile.com/pay-by-the-day-cell-phone-plans [nofollow] T-Mobile USA Minutes/PAYG SIM Optionshttp://prepaid-phones.t-mobile.com/pay-as-you-go-plans [nofollow] I have looked into this a lot, so reply here or shoot me a PM/email with any other questions.