No, you have to be a UK, Irish or qualifying Commonwealth citizen to vote in the UK parliament elections. I could get UK citizenship if I were willing to part with more than £1,000 and also give up my Norwegian citizenship (since Norway doesn't generally allow double citizenship), but I must admit my homeland, for all its faults, is more dear to me than the UK, so that is not an option, at least not for now.Why haven't you become a voter? Haven't you lived here quite a long time?! I thought you said you voted in the Brexit vote for some reason.
Likewise, you had to be a UK, Irish or qualifying Commonwealth citizen to vote in the UK's EU referendum. However, I did vote in the EU membership referendum of 1994 in Norway ...