Just been quoted £300 parts and labour to replace an old fuse
box with new consumer unit. Is this a reasonable quote?

It is pretty much a going rate, AIUI.

The parts are only about £50 but I believe the new part-p
regulations prevent me doing the work.

Part P doesn't prevent you doing the work. However, if you do so legally,
you'll have to pay for an inspection, which might not be cheap.

Christian.