Gardening TV show Ground Force is "probably coming to the end of its life", said BBC director general Mark Thompson after calls for it to be axed.
Dimmock, Titchmarsh and Walsh presented the show until 2001
The show which began in 1998 was "very good", he told BBC Radio Five Live.
"But some years later there are copycat programmes of Ground Force and Changing Rooms around and I think it's time to try something new and fresh."
On Wednesday, a government Green Paper said the BBC should not "play copycat" or "chase ratings for ratings sake".
"It's very important when a programme is reaching the end of its natural life that you move on before it becomes tiresome to the public," Mr Thompson said.
"I think the public do get very cross when they see the BBC flogging a dead horse."
Ground Force was originally presented by Alan Titchmarsh, Charlie Dimmock and Tommy Walsh, but Titchmarsh quit the show in 2001.
Last year Walsh announced he was also leaving to front his own series.
Changing Rooms was axed by the BBC last August after eight years.
Mr Thompson said: "The public want ambitious programmes from the BBC and real originality.
"What they don't want to see - which has happened occasionally, not often, but occasionally - is to see a programme on Channel 4 or Five and then to see a programme that looks a bit like it turning up on the BBC a few months later."
The BBC owed it to the licence fee payer to spend their money on quality programmes instead of chasing ratings, Mr Thompson said.
"The BBC gets the licence fee from the public. It doesn't have to take cynical or commercial decisions, it should really put its money where its heart is," he said.
Mr Thompson told BBC Radio 4's Today Programme that he did not believe this would be the final Royal Charter to renew the licence fee.
"Each time when alternatives are looked into by the people who consider these things, they end up concluding that the licence fee is the best of the available options," he said.
"The research the DCMS has done has concluded that the public are still very keen - as well as having a big, open market - in having a strong and independent BBC funded by the licence fee.
"I believe that in 2012, and beyond 2012, that may well still be the case."
On Wednesday, three trade unions launched a campaign to oppose BBC plans that would cut at least 2,900 jobs.
"I think the debate there is whether you save the BBC by keeping it exactly as it is now, or by transforming it to meet the challenges of this next digital period," Mr Thompson said.
"What we are trying to do is to use as much of the licence fee as we can on content firstly - rather than on overheads and bureaucracy - and secondly to try and find the investment to take advantage of these new digital platforms.
"That does mean some tough choices now."