I wish people wouldn't respond to posts like this with "I think...". There is so much misinformation out there when it comes to subjects like these.
1. Au is the only major CDMA provider in Japan. Softbank and DoCoMo are GSM.
2. All iPhones since the 3GS (except for the Verizon iPhone 4 CDMA version) are universal and with few exceptions, and provided they are unlocked, will work almost anywhere.
3. Many carriers will unlock you iPhone once it's paid for. It's done through apple, and when you pay for the unlock, it will be unlocked the next time you plug it in to iTunes (I've personally done this in Canada with an iPhone 4 and then used the phone in Japan).
4. Softbank does NOT offer this service, even when your phone is paid for. Check here before you reply with a "well, they should.."
http://support.apple.com/kb/HT1937?viewl...cale=en_US
5. Jailbreaking can be done on most iPhones, as long as you haven't updated to iOS 5.1 yet.
6. Unlocking on your own requires jalibreaking. If you haven't updated to iOS 5.1 yet then you can jailbreak. BUT, if you've updated your phone in the last year or so, then your "baseband" software on the phone would have been upgraded and there is no software unlock that will work. I am 99% sure that your iPhone 4 cannot be unlocked.
7. There is one option left: the gevey sim. But it will also only work if you've not updated to iOS 5.1 yet. It also requires you to dial "112" -an emergency number- whenever you reboot your phone. Not cool.
http://www.iosnoops.com/2011/03/27/gevey...-4-unlock/
The short answer is that no, it will not work in the UK. It is possible that someone will hack the phone one day to allow you to unlock it, but it's unlikely. The $75 alternative gevey sim method might work if you haven't updated your phone lately, but it's sketchy and will likely not work for long.
Take my advice and sell the phone in Japan before you move to the UK, and then buy a new one. You will be saving a lot of headache.