How much does the popularity of politicians depend on appearing on mainstream media?

This weekend, Alastair Campbell, the People’s Vote campaigner, said there was “something seriously sick going on inside the BBC”. This was after the BBC had Nigel Farage, leader of the Brexit Party, on Question Time on Thursday and on The Andrew Marr Show on Sunday, but dropped Heidi Allen, interim leader of Change UK, from Have I Got News For You on Friday.

I suspect Campbell knows this is not as biased as it looks. He knows the BBC takes a lot of trouble to observe its charter requirement of impartiality. Someone will be keeping a tally of the airtime given to the representatives of various parties during the European election campaign.

Allen – and Hat Trick, the makers of Hignfy – fell victim to a rather obscure Ofcom rule against “new appearances” by candidates or representatives of parties in “non-political programmes”.

But beyond that, Change UK will have been represented on news and politics programmes roughly in proportion to its opinion-poll support – although that is currently running at an average of one seventh of the Brexit Party’s support.

So, for every time we see Allen, Chuka Umunna or Anna Soubry on TV, we should see Farage seven times. On that basis, it is the leader of the Brexit Party who is probably under-represented.

It doesn’t feel like that because he is news. Journalists are interested in him, and Andrew Marr’s interview with Farage attracted a lot more further coverage than those with Marr’s other guests, Damian Hinds, the education secretary, and Jonathan Ashworth, the shadow health secretary.

So the secondary reporting of and comment on Farage’s interview by other media organisations, such as The Independent, which are not governed by Ofcom guidelines or royal charters, was “biased” in the amount of attention devoted to him.

But a lot of that secondary coverage was uncomplimentary. Our own Tom Peck said: “Nigel Farage has been a public fraud and phoney for decades.”

There isn’t an arithmetical relationship between the amount of exposure on broadcast media and a politician’s popularity, therefore. Politics and media are a complex web of feedback. The Brexit Party is popular mainly because we haven’t left the EU, not because Farage is on TV a lot.

But Farage being on TV gives him the chance to rant and bulldoze about “BBC bias”, which plays well with his supporters and reinforces their support. He is good at this, as people such as Alastair Campbell ought to accept, however grudgingly, being good at the communications business themselves.

Change UK has been less good at communications, with various name-changes and a ridiculous battle bus, but its main problem is of substance rather than style. Its “second referendum to stop Brexit” message has been drowned out in competition with the Liberal Democrats and the Green Party.

As a result it has less public support and therefore its spokespeople are entitled to less airtime.