Dermot O'Leary (left) and Tony Blackburn (right) hosted the shows
The BBC has been fined £95,000 by media watchdog Ofcom for broadcasting 13 quizzes which listeners could not win.
The competitions ran on eight editions of Dermot O'Leary's Radio 2 show in 2006 and five Tony Blackburn programmes on BBC London 94.9 in 2005 and 2006.
All were pre-recorded, however, so there was no way to take part in them.
These were "serious" breaches and on-air apologies were needed, Ofcom ruled. The BBC "accepted" the findings, saying procedures had since been tightened.
Radio 2 was fined £70,000 for eight breaches between June and December 2006 and told to broadcast the watchdog's findings on-air "at a time, and in a form, to be decided by Ofcom".
OFCOM'S LATEST FINDINGS
BBC Radio 2 - Fined £70,000 for "fake" competitions on eight Dermot O'Leary shows
BBC London 94.9 - Fined £25,000 for "fake" competitions on five Tony Blackburn shows
BBC One - Blue Peter criticised for deceiving viewers by altering an online poll to name a cat
BBC Asian Network - Film Cafe breached code by changing the winners of two film awards
BBC 6 Music - Tom Robinson Show criticised for inventing a winner for concert tickets
O'Leary's Saturday afternoon show was pre-recorded on these occasions "due to the presenter's other work commitments", it said.
When the competitions were run, winners were selected from listeners who had contacted the show via the programme's website or newsletter, it added.
BBC London 94.9, the BBC's local radio station for London, was given a fine of £25,000 and must also read the findings on-air.
Again, the breaches occurred when Blackburn's Saturday lunchtime programme was pre-recorded, on five occasions between December 2005 and December 2006.
Ofcom said listeners who had previously contacted the show were invited to be the competition entrants.
The watchdog added it was "very concerned by the repeated, pre-meditated and deliberate decisions to include competitions in pre-recorded programmes that were broadcast 'as live'".
These decisions were made for purely "logistical" reasons, it added, and not because something had gone wrong.
And therefore production teams "knowingly misled" BBC audiences as a result, it said.
Ofcom also said it was "wholly unacceptable" that the BBC had known about these breaches but had decided they were not serious enough to be declared in a previous "trawl" of mistakes.
As well as Ofcom's investigation, the BBC Trust - which effectively acts as a watchdog for the BBC - launched its own inquiry into the quizzes.
"These competitions were run unfairly and therefore did not match the expectations of the likely audience," the trust said in its report.
The cases were "serious" and "did involve audience deception" because listeners were "misled", it added, and demanded on-air apologies were broadcast.
In response to the two reports, the BBC issued a statement saying that "these historical breaches were tackled by a comprehensive action plan launched by the BBC in July 2007".
"This included a major programme of training for over 19,000 staff, a new specialist unit to provide advice on all technical aspects of running competitions and a strict new code of conduct.
"We welcome Ofcom's recognition of the extensive action taken to address these issues and that neither the BBC nor any member of staff made any money from these lapses."
Blue Peter introduced Cookie the kitten (right) after the row about Socks (left)
Both stations will broadcast apologies at about 1400 GMT on Saturday.
Also on Thursday, Ofcom released its judgements on a number of other matters, including the furore over the naming of a cat on Blue Peter.
The BBC One show's production team rigged an online poll in 2006, in which the winning entry - Cookie - was disregarded in favour of the name Socks.
The watchdog has now ruled this was another "serious" deception, "especially given that the programme is primarily aimed at children".
However, there was no financial penalty attached to the ruling.
Separately, the BBC Asian Network's Film Cafe programme was criticised for a "lack of regard" for Ofcom's broadcasting code.
During its Bollywood film awards in February 2007, the announced winners of the categories for best actress and best supporting actress were not the stars who received most votes from listeners.
In the best actress category, the award was switched when an interview with the true winner fell through, while voting figures were "misread" for the best supporting actress category.
A name was made up on Robinson's show when nobody entered a contest
Ofcom said there had been "a willingness to exploit audience trust in the programme and knowingly mislead viewers".
And the Tom Robinson Show on BBC 6 Music was also judged to have breached Ofcom's code after making up the name of a competition winner in September 2006.
A group - whose name was not given by Ofcom - had been interviewed on-air and unexpectedly offered listeners a pair of tickets to a gig.
Nobody phoned in and "in order to spare the band, the programme and the presenter any embarrassment, the producer invented a winning name, which was broadcast".
Ofcom said this desire to protect people's feelings was "misguided" and should not have taken "precedence over audience trust".