The Great British Bake Off co-host Sandi Toksvig is among more than 30 prominent humanists who are making a fresh appeal to the BBC to open up Radio 4’s Thought for the Day to non-religious voices.

The bid to reform the daily slot is also backed by the philosopher Julian Baggini, the scientist Alice Roberts, the comedian Ed Byrne, the human rights campaigner Peter Tatchell, the Labour MP Nick Brown and the Conservative peer Tristan Garel-Jones.

They are among 33 patrons of the charity Humanists UK who have signed a letter calling on Tony Hall, the BBC’s director general, calling for the ban on humanists presenting Thought for the Day to be lifted.

The 165-second slot, aired each morning at about 7.45am on the Today programme, has irked atheists and humanists for years. Critics point to the growing number of people in the UK who do not identify with any organised religion, arguing that a slot devoted to reflections on issues of the day should not be restricted to people of faith.

The letter, published in the Guardian, says: “Over half the British population do not belong to any religion and around a quarter have a humanist worldview. By barring humanists from Thought for the Day, the BBC is blatantly failing in its remit to reflect the diversity of beliefs of its audience and wider population, and its legal duty to treat non-religious and religious beliefs equally.”

It adds: “To many, the exclusion of humanists from Thought for the Day sends a very clear message that humanists do not have as much to contribute as religious people to one of the BBC’s most high-profile ethical slots.”

Humanists UK has campaigned for 16 years to open Thought for the Day up to non-religious voices. Last year, the corporation’s review of religious and ethics output rejected any change to the format, saying it and Pause for Thought – a similar item on Radio 2 – would “continue as religious slots in primetime radio, with speakers from a wide range of faiths reflecting on an issue of the day”.

The review added: “We will also continue developing the stable of contributors with voices from different communities and religious traditions, including younger voices and women.”

Andrew Copson, the chief executive of Humanists UK, said the BBC had “blatant disregard” for non-religious people who wanted to contribute reflections but were barred from doing so.

“It is deeply concerning and frankly undemocratic that, despite decades of humanist and secular campaigning to reform Thought for the Day, the BBC still will not budge and instead continues to shut out our voices time and time again.”

Last year, John Humphrys, the veteran presenter of the Today programme, caused a stir when he described the slot as “deeply boring”.

In an interview with the Radio Times, he said: “It seems to me inappropriate that Today should broadcast nearly three minutes of uninterrupted religion, given that rather more than half our population have no religion at all.”

He said if it was a slot for secular reflection, “I’d have less of a problem with it. Why can’t you have an atheist? Or an agnostic?”

The majority of contributors to Thought for the Day are Christian, although there are regular Muslim and Jewish contributors and occasional Hindus, Sikhs and Buddhists.