Any good guidance out there that we can collate? A few thoughts from me below... https://twitter.com/rebeccamjohnson/status/1358395688204328960
Check the systems for applying for a PhD place, and applying for funding. They're usually separate in the UK, and it's almost always more straightforward to get a place than to get funding.
When applying for the PhD itself, it's a good idea to write to prospective supervisors. You'll get a sense from that of whether they're keen on the project, and also of the kind of supervisory relationship you might begin to build with them.
Many prospective supervisors will be happy to give some feedback and advice on proposals -- and to chat about the 'fit' section for funding applications, where it can sometimes be difficult to know the full details of what goes on at a given institution.