I get a good deal on my breakdown cover through my car insurance. (That's the only reason that I'm with the RAC. I've had good service from both the AA and Autonational Breakdown in the past).
The AA's procedure for getting a quotation seems simple enough. You simply need to tick the relevant boxes here:
https://www.theaa.com/breakdown-cover/uk
The RAC's website allows you to build your cover, step-by-step, here:
https://www.rac.co.uk/breakdown-cover/join-uk-breakdown/build-cover-vehicle?version=vbm-only-mthly-desktop
Autonational Rescue keeps it simple, here:
https://autonational.co.uk/products/
Green Flag (which I know has plenty of fans among AB members) does seem to want to know rather more information though, including your vehicle's registration number and, rather oddly, your date of birth:
https://buy.greenflag-breakdown.com/quote/#/start