Sceptical MPs have joked it is becoming "a cult in parliament", but mindfulness meditation stepped into the political mainstream on Wednesday when MPs and peers gathered at Westminster, closed their eyes and went silent for a minute.

Joined by the comedian Ruby Wax, now the poster girl for the benefits of mindfulness to overcome mental health problems, politicians including former ministers Lord Haworth and Jim Fitzpatrick straightened their spines and focused on their breath at the launch of an all party group to explore the potential for mindfulness in health, education, criminal justice.

"Connect with the breath, wherever it feels most strong," intoned the meditation. "For the full duration of the in-breath and the full duration of the out-breath."

It was just a taste of what 95 MPs, peers and parliament staff have already experienced on mindfulness meditation courses inside parliament. The practice – based on Buddhist meditation but updated for secular users – is catching on across a stressed-out Britain.

Mental health problems are estimated to affect one in four and academic studies claim mindfulness can affect a 20% reduction in symptoms of anxiety and depression. If practiced regularly, proponents report it develops "in the moment" and non-judgemental attention which prevents people becoming caught up in anxious or depressive thoughts.

Its popularity has spawned more than 800 courses nationwide and a Headspace meditation app with 50,000 paying users. The most popular guide book is selling 2,000 copies a week and mindfulness based cognitive therapy is now recommended by the NHS to prevent relapses into depression. Now politicians are falling back on it too.

Lord Andrew Stone told the meeting he used it to steady himself after he became "scared" when he was dispatched to Cairo for meetings with Egypt's military leadership earlier this year.

"I didn't know how to cope," he said. "But these practices made a massive difference. I was talking to some pretty serious people there, but I was being compassionate to all sides."

Co-chair of the group, Tracey Crouch MP, one of only a small number of MPs to publicly admit using anti-depressants, revealed mindfulness practice had helped her come off the drugs.

"I have given much better speeches in the House since I started mindfulness," she said. "We genuinely can turn the UK into a mindful nation."

Chris Ruane MP, Crouch's co-chair said some MPs had not come to the parliamentary mindfulness sessions "because they are afraid of being stigmatised".

"I have friends who come by and say 'Om' [a Buddhist incantation]," he said. "They think we're creating a cult in parliament."

He said more MPs and peers were joining up, and the potential of the practice had captured the attention of Liz Truss, the education minister and Andy Burnham, the shadow health secretary.

Wax told the MPs that mindfulness could even help them win votes, by helping them focus on voters when they are campaigning rather than appearing distracted.

"The voices come to everybody's mind," she said. "'I could have, I should have, I am going to fail'. Mindfulness is a way of cooling that engine."

But there are concerns. "There is still no quality control and there is no standards people need to stick to to deliver this important therapy," said Dr Florian Ruths, clinical lead for mindfulness at the Maudsely hospital. "I worry that quite vulnerable people with quite serious problems might being going to courses led by people who aren't aware of the consequences."

Nevertheless it was the testimony of a group of school children, thousands of whom have been exposed to the practice in the last few years, that most moved the politicians.

"Just over a week ago my grandad died," Catrin, a year five pupil from a Colywn Bay primary school said. "Mindfulness practices allowed me to be in the here and now. It helped me to be calmer and accept what had happened."

Ciaran, a year six pupil at the same school, said he had been worrying about moving from Wales to York with his family.

"Mindfulness has helped my story-telling mind worrying about what will it be like? Am I going to like it? What about my friends. Mindfulness has helped me be in the here and now, enjoy it and not worry about what might happen."