The UK stock brokers section now also has a comparison table for stock brokers that offer personal CREST accounts. If you’re unsure what personal CREST membership is, CREST is the UK’s central securities depository and you can find an explanation of why you might want a personal account there in the notes under the table.
There aren’t that many stock brokers that do this. The table lists the six main ones; some of the other traditional full service stock brokers may offer CREST membership as well, but are unlikely to be any cheaper. Other firms will be added if I get concrete details (many traditional brokers tend to be vague about fees, operating “by arrangement”, which makes compiling comparison tables awkward).