The post you are reporting:
QUOTE FROM BARRY W: "John Nott did resign over the Falklands accepting full responsibility, as the Sec of State, for mistakes by the MOD in the run up to the Falklands War. Those were the days when Ministers were expected to do such things, take responsibility that is, something abandoned when Labour come to power. We are yet to see if this honourable precedent will be resumed by the coalition, I hope so." UNQUOTE
John Nott did not resign. He very reluctantly offered his resignation but was kept on by Margaret Thatcher. As Howard says, he made regular appearances on TV during the Falklands Conflict which must have particularly galling to the Navy which was fighting the war which his announced naval cuts had precipitated. He retired from politics the following year and was knighted.
You may be thinking of Keith Speed, the Navy Minister. He strenuously opposed Nott's proposed cuts prior to the Falklands and finally felt constrained to make a speech to that effect in the House of Commons. He was thereupon asked to resign and, when he refused, was personally dismissed by Margaret Thatcher.
Alternatively, you may be thinking of Lord Carrington, who did indeed resign as Foreign Secretary. John Nott's take on this was: "The Falklands had been invaded and I was the Defence Secretary. I therefore felt some responsibility. I said: 'This puts me in an impossible position. Peter Carrington looks like an honourable man and if I don't resign, I'll look like the dishonourable one.' So I sent my resignation over. But Margaret Thatcher persuaded me to stay on, saying the Falklands were really the responsibility of the Foreign Office."
