I don’t think there is anything stopping you doing your own conveyancing but if you have a mortgage, they’ll instruct a solicitor to do their element which normally your solicitor would do on their behalf.
It also assumes you know what you are doing and given how little it actually costs, it’s really not worth it. A big chunk of the fees you’ll end up paying anyway for surveys, searches etc.
You may get a few raised eyebrows from others in the chain too and they may not deal with you without a solicitor onboard. I’d certainly be asking questions about it.
@Skillmister is a conveyancing solicitor iirc