I just got a Samsung S5620 from Tesco mobile PAYG (£120). It's got wifi and a few other (not so useful!) features. The HTC Desire, to me, is a far better phone, but also a lot more expensive.
It's not too big and the Tesco 'triple your credit' makes it economic for me.
Wifi won't cost you anything on any phone bill, but take care that you can find a free wifi hotspot. There's usually one around, whether it's intentional or not ;)