I work a lot with GP practices, alava - all of them have a formal complaints procedure these days, they have to. You need to write formally to the practice manager who must respond and investigate, and give you a reply within a given number of days (I think it's 28).
There is a national shortage of GPs, this is why receptionists (even at my practice) gatekeep when people ring up, to try to save expensive GP time. If you can be given a telephone consultation with a nurse or GP, that's a great deal more cost-effective than a GP appointment if that's not strictly necessary. If you have nurse practitioners at surgeries, they are highly trained, many can prescribe - it's not always necessary to see a GP. It's not always necessary to see a GP to get test results, but the GP looks at the results, if they need to see your wife they will call her in, and if the GP has asked to see her it can be prioritised.
If you complain formally (and swearing doesn't help, all surgeries have a zero tolerance policy against aggressive patients) then your complaint has to be investigated. However, if you think it's the surgery rather than the system, then change GPs. It's easy enough to find out which other local surgeries are taking new patients, and it's easy to move these days.