I've tried various UK outfits. When I was in AA I spent ages waiting, then if they couldn't fix it, ages more waiting for a 'relay' vehicle to carry us and car home. I was also in RAC for a while. But when my daughter learned to drive I started looking for the cheapest that would cover her as well and found Green Flag.
They cover the car, whoever is driving it (and for a little extra you can get personal cover for self and spouse in any car), whereas AA covers the person (extra to put another person on).
I changed because of the cost but found the service SO much quicker. Green Flag is the one many car dealers give you 'free' for the first year.
And as I'm over 55 I can get membership cheaper through SAGA. And my insurance, also through SAGA has a useful clause (never used yet) that covers anyone to drive in a medical or motoring emergency.