[peppery-idiot]

Three month notice periods are relatively common in the UK, don't worry about it -- and don't quit before you have another job lined up.

Your proposed course of action is predicated on a hypothesis, that no employer wanting to make you an offer because of your notice period, that has no supporting data. Anecdotally, nobody worth working for (and plenty of companies not worth working for) care about a 3 month notice period.

I'd say put the feelers out there and interview casually for a while before writing yourself off because of your notice period.

Also, I don't know if other commenters are based in the USA where it seems common for employers to practice retaliatory firings.

In the UK if you have more than 2 years of service at your current employer, it's very very unlikely that they can fire you without a negligence/misconduct claim against you. You're more likely to be put on paid garden leave, or somehow made redundant (but you should be paid a lump sum).