Owning your own home

What are people's thoughts on using an estate agent's (Dexters) recommended conveyancer? I like the idea that there will be a good line of communication between all the parties, especially in a chain. Any major downsides or horror stories, aside from potentially higher costs?

Any upside from a connection with the EA is an illusion.

If they are cost competitive and don't sound awful on the phone then do some more research and see what other people say about them. It is likely they will be a 'farm' type operation but that's not a bad thing in itself although it might be a crap shoot on who will be assigned to your work. And if it is a farm, be aware that any online reviews apply to a specific person who handled a case, not the organisation as a whole, so the value of the review becomes very low.

Not worth it - I'd seek independent conveyancing

Also as above I can list out a load of conveyancers I’ve spoken to this week with some recommendations based on my initial ‘screening’.

Once the solicitor's start talking then the main use for the estate agent is just keeping you updated on the other bits of the chain. You can't (legally, or just generally in my experience) rely on what the estate agent's are saying so ultimately everything needs to go through the solicitor.

My solicitor didn't speak to the estate agents at all and that didn't cause any issues for me. (The estate agents bitched and moaned about it but without any good reason).

tl:dr Pick a good solicitor, someone who is easy to get hold of and can answer your questions and progresses things quickly. That probably isn't the one recommended by your estate agent.