In all cases that I can think of, the minister is told to resign, and they do so. Even in cases when it is clear to everyone that the Minister has been fired, it is presented as a resignation1. Consider the sacking of Damien Green. He writes:
I regret that I've been asked to resign from the Government following breaches of the Ministerial Code, for which I apologise. It has been a privilege to serve ...
and May replies
It is therefore with deep regret, and enduring gratitude for the contribution you have made over many years, that I asked you to resign from the Government and have accepted your resignation.
It's not clear if a minister would have even theoretical recourse to an industrial tribunal (*edit as Will notes in another answer, they don't) , as appointments are made (in theory) by the Queen, rather than by a contract between an organisation and an employee. In practice, all ministers know that they can be fired without notice. There is no protection from unfair dismissal that a normal employee would have.
A Prime Minister can remove a minister for any reason or for none. In the occasional "reshuffles" a Prime Minister may decide that they just want "new blood" and ministers can get axed without warning. Generally, ministers get sacked for breaching the Ministerial Code, or for bringing the government into disrepute. If you're not winning support for the Government, you may not last long in your post.
As a ministerial position is a paid position, ministers who resign or are reshuffled do receive severance pay, as are ministers who lose their position following an election.
After a minister has been sacked, they remain an MP and thus continue as a backbench member of parliament until the next election. If a Minister has done something wrong, they may also be ejected from their parliamentary party (called "having the whip removed") but would still be an independent MP and cannot stand as a member of their (former) party at the next election.
Originally MPs couldn't resign (having been elected, not appointed) but there is a procedure in which an MP is "appointed as Steward and Bailiff of the Three Hundreds of Chiltern" (or another similar post) which is a Crown office with no responsibilities. Since MPs cannot hold Crown offices, being appointed to the Chiltern Hundreds effects the MP's dismissal from Parliament.
1 The sacking of Gavin Williamson is an exception to this. The PM told to leave the government. His response clearly denies any wrongdoing. This is an unambiguous example of a sacking, which has not been presented as a resignation. The exceptional nature of the case is an example of the exceptional state of British Politics in 2019