Any phone that supports the world 3G standard frequency of 2100 MHz will work in Japan.

I have no idea what a 4 quad is, but I think you mean quad band GSM. That's correct; it won't work there if it's only quad band GSM. But many many phones are quadband GSM and 3G 2100 MHz. As long as the specs say that the phone supports "UMTS 2100" or "WCDMA 2100", you'll be fine. Any 3G phone you buy in the UK will almost certainly be such a one.

Also, make sure whatever SIM you buy allows international roaming in Japan. Many prepaid SIMs don't.