Tony Blackburn has reiterated his dismay at being sacked by the BBC following the Dame Janet Smith report into Jimmy Savile, and says that if there was a suspicion of misconduct surrounding him in 1971 he "should have been investigated."

The former BBC radio presenter was sacked because, according to Director General Tony Hall, his evidence "fell short" of what was required by the Savile investigation. However, Blackburn says that it is his belief that the BBC 'fell short' by not investigating him, following a complaint by the mother of 15-year-old Claire McAlpine.

"I am saying that the management of the BBC at the time did fall short of my standards," he told BBC Radio 4's Broadcasting House programme, "because I should have been investigated. I didn't do anything wrong I hasten to add, but I still should have been investigated if there was a complaint against me."

McAlpine committed suicide after claiming in a diary that Blackburn had seduced her. Dame Janet's report cites testimony that Blackburn was interviewed by both senior BBC manager Bill Cotton and Sir Brian Neill QC over the alleged complaint.

However, Blackburn insisted that no such meetings took place. In consequence, Dame Janet's report rejected his evidence given during the inquiry, and Tony Hall said that as a result he "felt it was untenable for the BBC to continue its relationship [with Blackburn] because of that."

Blackburn said in the Radio 4 interview that he was given an opportunity to resign voluntarily and then return to the BBC "in a few months", an offer he rejected. "I've got nothing to hide and they are sacking me for telling the truth," he said. "It's as simple as that. So why would I want to resign from a job that I absolutely adore?"

The presenter said again that he was never asked to a meeting with BBC management over the complaint in 1971, despite what the memos cited in the Dame Janet report suggest.

"I'm sure there were memos written in 1971, but I never saw them," he said. "The truth of the matter is I've seen the memos, but there's nothing to go on with them, and I've said time and time again, 'Can you show me any notes at this meeting that I'm meant to have been at?' and they haven't got any," he said.

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"What I'm actually basically saying is, and this is what the BBC is slightly upset about, I think I should have been investigated for God's sake. If I'd done something wrong, then I should have been investigated, but unfortunately, I only heard about this in 2012 I think it was, and the BBC were aware of that, but I never saw these memos."

Blackburn said that the actions of the BBC had left him with little choice but to challenge the corporation over the issue: "I don't want to sue the BBC, I've no wish to do that, but I do want to get my career back, and my reputation back."

But he added that he did not hold much hope for a comeback. "Probably not," he said, when asked whether he expected to return to the BBC. "Because I don't think the BBC upper management are big enough to go, 'This is a mess, we've made a mistake.' And I think they have made a mistake, I think it's backfired on the BBC."

The BBC and Radio 2 controller Bob Shennan declined to be interviewed for the programme. A BBC statement read, "Clearly Mr Blackburn and the BBC are in disagreement on a range of issues. Our position hasn't changed. As matters are potentially subject to a legal process, we have nothing further to add at this stage."

Listen to Tony Blackburn's interview with BBC Radio 4 in full here