Free TV licences for over-75s could be limited to those who live with someone else also over the age of 75 in a plan being considered by the BBC that could save it about £150m a year.

It comes as the corporation tries to work out how to shoulder the £650m-plus sum of paying for the free licence fees from 2020, which it had to agree to as part of a funding deal with the government.

The BBC is compensated by the Department for Work and Pensions for the television benefit. But from next year the subsidy will be phased out and by 2020 the BBC will foot the whole bill, which will cost the corporation about a fifth of its £3.7bn income.

By not giving free licences to over-75s who live with someone who is not eligible for the benefit – such as a spouse or partner under the age of 75 – it is thought the BBC could save about £150m. That is almost the equivalent of the combined annual budget of Radio 4 and BBC4.

Frontier Economics, the consultancy chaired by the former cabinet secretary Lord O’Donnell, has been considering for months how the BBC could mitigate some of the cost. Another option is means-testing those eligible for the benefit.

While any limitation to the free deal could be controversial, it is also likely to draw sympathy from some audiences who may be happy to forgo their free licence if it helps secure the future of their favourite public service shows and channels.

The BBC faces increasing competition from commercial rivals, such as US companies Netflix and Amazon, for talent and programmes – and controversially, the corporation lost The Great British Bake Off to Channel 4 last year.

Footing the £650m-plus bill – which successive governments have tried to foist on the BBC since 2010 – will put the corporation under further financial pressure.

A BBC spokesman said: “As things stand, the BBC doesn’t have any plans to change the current policy … the Digital Economy Act transfers control over free TV licences to the BBC in June 2020.”