Whenever I need cover, I call British Gas. I take the deal whereby I pay them a certain amount, maybe 99 pounds or something like that, and sign up for one years cover. I then always cancel the cover at the end of the year, and do no maintenance until the next time it stops working.
In theory they have three different fixed prices they charge for a repair, depending on how many hours it takes, but I've never gone wrong in assuming that it's going to be the longest option.
The overall cost works out in the same ball-park, a bit more expensive, than they charge for their longest fixed price repair. So a few hundred pounds. But by signing up for a years cover, if the repair doesn't work, I can keep calling them up for as many times as it takes, until the problem is actually fixed.
To be fair to British Gas engineers, I've had the same (expensive) boiler problem fixed several times over a 20 year period, and only one time did they not fix it properly the first time. That one time, they did eventually do the expensive repair I guessed was required, after a couple of call-backs.
On the most recent occasion, they determined from their database that the cause of needing the boiler circuit board replacing was an incompatibility with a pump they had installed several years earlier, so they replaced the board and the pump.