Hi and welcome to KH!
It might be best to start with a pattern. It'll recommend a needle size and a bead size if beads are part of the pattern. As you do more lace knitting, you can buy needles in more sizes. There should be lots of patterns on Ravelry (free to join) or at Knitting Pattern Central. At least those sites will give you an idea of what's available.
Here's one source for small needles but of course, one in the UK would be better for you.