Matthew, the best two places for UK dance listings are those on: ballet.co
, which has the advantage of coverage of the UK and londondance.com
, which covers the smaller as well as the larger venues in London.
Both these sites have good search functions.
Depending on how wide you cast your net in terms of dance styles, I'm sure you will be able to find interesting dance in London. Liverpool might be more tricky. Here's one "what's On" for Liverpool and you will find more on Google.
As your visit draws nearer Matthew have a look to see what looks good.