The 77-year-old said there was a “BBC agenda” of having to include people of colour and disabled people on shows, which he described as a “fairly futile exercise”.
Rees had presented the popular programme since 1976 and hosted more than 500 episodes with guests including Dame Judi Dench and Sir David Attenborough.
All I want is people on the programme who can do it. Who are up for it. Who can be amusing and witty and literate, and never mind what colour they are
He presented his final show on Boxing Day.
Rees told the PA news agency: “One is the BBC’s agenda of prescriptive requirements as to who I would have as guests on the programme.
“The second aspect of wokery is the interfering with my choice of quotations, rooting them out for reasons of a woke nature.
“The one in the newsletter that I give is the Noel Coward quote, which they said was reflecting colonial attitudes which I don’t think it is actually.
“They leant on me to leave that out and substitute something else. So it is that sort of thing that, taken together with the other reasons for ending the show, is what it is all about.”
A segment in which Rees planned to ask guests to identify the lyrics from Noel Coward’s 1931 song Mad Dogs And Englishmen was scrapped after pressure from the BBC, he said.
The lines were: “In Bengal / to move at all / is seldom if ever done.”
Rees also cited the challenge of recording programmes during the pandemic and reaching his 500th episode as reasons for stepping down.
He said the BBC had begun to implement the new rules as part of a “creep”.
He added: “Over the last two or three years it has become noticeable that there was this sort of BBC agenda of having to include persons of colour, most recently people with disabilities on the panel, which I think is a fairly futile exercise.
“All I want is people on the programme who can do it. Who are up for it. Who can be amusing and witty and literate, and never mind what colour they are.
“So that was something that crept along, and I went along with it. But I was not very happy at doing so.”
He said the tipping point had come last summer when he had been given a list of potential guests “mostly made up of people either from an ethnic minority or from some sort of vocal minority – pressure groups and people like that”.
However, Rees said the BBC had been “extremely nice about my chucking in the towel”.
He said that ahead of Quote… Unquote’s final programme on Boxing Day, figures at the broadcaster “took me out for lunch, they showered me with gifts and made a great fuss”.
“So there was no rancour involved,” he said.
A BBC spokesman said: “We want our output to be representative of the UK and we want contributors on our comedy shows to be wonderfully engaging and funny.
“These two ambitions are not mutually exclusive and it would be highly condescending to suggest otherwise. We have creative, editorial discussion around every production and they are very much standard practice.”