How can I fix a bayonet light socket without replacing it?
Not really. The "teeth" are an integral part of the design and if weakened won't hold the bulb in place safely.

The best thing you can do is find an electrician who'll change the socket for you. It's a quick job so you shouldn't be charged much, but get 2 or 3 quotes to make sure you find the best.

If you're having problems with bayonet fittings then it might be worth getting it replaced with a screw cap. Even in the UK these are becoming more popular so you shouldn't have any trouble finding bulbs.