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The government-funded scheme, which provides free TV licences to older viewers, comes to an end in June 2020.

BBC chairman Sir David Clementi said the board, which will make the final call, “does not underestimate the significance of the decision, its implications for the BBC and its audiences”.

Options could include the BBC copying the government scheme and paying for it.

“But”, it writes, “that could cost around a fifth of our budget – the equivalent to what we spend today on all of BBC Two, BBC Three, BBC Four, the BBC News Channel, CBBC and CBeebies.

“That would mean over 75s would not have to pay, as at present, but we think it would fundamentally change the BBC because of the scale of service cuts we would need to make.”

Another option could be scrapping the free licence fee for over-75s.

“This would mean the BBC would not have to make significant cuts to BBC services, but would have an impact on those over 75s, particularly poorer pensioners, who currently do not pay,” it says.

The BBC says it could also reform the scheme in various ways including discounting the cost of a licence fee for older people, raising the age from 75 to 80, or introducing means-testing.

The broadcaster said that it was “not backing any particular option over another today”, as it opened a three-month consultation.

Its board “hopes to make a decision by the summer”.

BBC director-general Tony Hall said: “This is an important decision.

“We have set out a range of options – each has merits and consequences, with implications for the future of the BBC, and for everyone, including older people.

“We need to hear views to help the BBC make the best and fairest decision.”

Shadow media secretary Tom Watson called for the government to “step in and save TV licences for the elderly”.

“The government should never have privatised welfare policy in this way. Labour opposed this move from the start,” he said.

It is expected that free TV licences would cost £745 million a year by 2021/22.

BBC consultation on free TV licences for over 75s