Nokia are doing Lumia phones at all price-points now. They've got the 520, 620, 720, 820 and 920 at everything from £120 upwards. So you ought to be able to find one to fit.
I had a Lumia 710 on WP7 - which was perfectly nice - but I've not really used WP8, so don't know if the new cheaper ones will be fast enough. I'd expect it though, as that was apparently one of Nokia's aims. I've seen a lot of disappointing cheap Android ones, so the Nokia's have got to be worth a look.
The 710 wasn't brilliant on build quality (it was OK for the £120 I paid - but cheap for the £300 it was launched at). But I think the first lot of Lumia phones were outsourced, whereas this lot are built by Nokia, so hopefully better. I can't be any more help than that, as I've not played with them. Although isn't there also a cheap Huawei, the Ascend according to a quick search. Not sure how good though.