BBC Radio 4’s Today programme has increased its audience despite threats of a boycott from listeners who claim to be exasperated by the broadcaster’s political coverage.

The morning show continues to divide opinion about its interviewing style after the departure of the long-serving presenter John Humphrys, but its audience rose to 7.2 million listeners a week in the final three months of 2019, aided by interest in the general election campaign.

Since then Today’s editor Sarah Sands has resigned after the announcement of cuts to the BBC’s news output, while ministers are maintaining an increasingly uneasy boycott of the programme on the basis that No 10 believes it does not speak to the voters the government needs to win over.

The official quarterly radio listening figures from Rajar also show that Zoe Ball’s BBC Radio 2 breakfast show has lost about a million weekly listeners since she took over the slot from Chris Evans – whose rival Virgin Radio show has attracted about a similar number to the digital-only station.

Radio 1’s audience has hit a record low, as the station fights to attract younger listeners who are being lured away by other forms of listening. The station still reached 8.8 million listeners a week in the final three months of 2019, but is increasingly having to use different ways to reach its future audience. Research from the regulator Ofcom this week showed that radio use among five- to 15-year-olds has fallen from 26% to 22% in the space of a year.

The BBC’s head of radio, James Purnell, said: “The latest figures show some of the challenges we face across the radio industry with retaining a live listening habit amongst young people, whose audio consumption is rapidly changing. We are focused on keeping live listening strong and looking for new ways to do so, but we also want to ensure we offer more for our audiences however they want to listen.”

Despite the enormous growth of interest in podcasts, with the BBC increasingly channelling funds into the format, the audience for downloads is still dwarfed by the number of people who tune in to national radio stations in their millions.

Smart speakers such as Amazon’s Alexa are increasingly shaping listening habits, with many people replacing their kitchen radio set with such devices. This can change which stations people listen to, as users have to verbally prompt for their preferred station every time they turn the speaker on – rather than just leaving a radio set tuned to the same station.

The BBC’s national stations continue to dominate headline listening figures but commercial beneficiaries of changing habits include talk radio station LBC, which now reaches 2.7 million listeners a week and Absolute Radio, which has grown the audience its network of stations playing different music from every decade from the 1960s to the 2000s.