Yes, but you are expected to write a nice thank you for firing me letter to the Prime Minister who after much soul searching will accept.
One of Mrs Thatcher's ministers refused to play the game - his resignation letter consisted of one sentence, along the lines of "Margaret, you have ordered me to resign, so I am resigning." Unfortunately i can't remember who it was at this distance...
But looking at it from a purely cynical point of view, surely a lot of resignations would have gone down a lot better if they had been properly fired instead. It lets the Prime Minister show authority and an unyielding attitude to corruption or incompetence. Quite apart from the principle of sometimes someone does something so bad surely they don't deserve the dignity of getting to jump themselves.
I think there are two problems with this - firstly, the prime minister usually wants to keep open the possibility of recalling the miscreant at some point in the future (something that was taken beyond the point of satire by the last Labour government with Mandelson's revolving door resignations), even if only to encourage the resignee to remain loyal. And secondly, firing them for gross incompetence/corruption/criminality will call into question the prime minister's judgement for appointing them in the first place. Best to let them spend more time with their family/concentrate on clearing their name/draw a line under the controversy etc.
As for the actual question, most reshuffles usually see at least one or two ministers being given the opportunity to support the government from the back benches. This is usually a firing, but one that's done under cover of a reorganisation. I can't remember the last time a minister was fired without such cover though.