Boris Johnson was booed by an angry medical student as he left a Cambridge hospital while on a visit, where he set himself a new Brexit deadline of leaving the EU by January “at the absolute latest”.

The prime minister appeared to get a frosty reception at Addenbrooke’s hospital, where staff were not given advance warning of his visit and national media were not invited to attend.

He was confronted by Julia Simons, a 23-year-old medical student, who later criticised him for using the hospital for a “PR stunt”. “Staff were not informed even when he was in the hospital. He was too cowardly to face the uncensored opinions of staff because we know the reality the effects of his government’s and party’s policies on patients,” she said afterwards.

Johnson also went to a primary school in Bury St Edmunds and a police training college in Hendon as he attempted to shift the focus to his domestic agenda.

In a broadcast interview, though, he was forced to address criticism for failing to meet his deadline of taking the UK out of the EU by 31 October. “There are just too many people who are basically opposed to Brexit, who want to frustrate it,” he said.

“It was the mandate of the people. They voted by a pretty substantial majority to do this and parliament has simply stood in their way.” He also recorded a shaky handheld video of himself travelling in a car, released on social media, accusing Labour of blocking Brexit and while “they couldn’t block parliament actually voting for the deal, they did vote for a delay”.

The claim that parliament voted for his Brexit deal was highlighted by Tom Watson, the Labour deputy leader, as one of 12 key lies that Johnson was already propagating in the election campaign.

On Thursday night, the senior Labour MP wrote to broadcasters asking them not to repeat Johnson’s untruths during the election campaign, branding him a peddler of “fake news, lies and distortions”.

He said as part of the “serious matter of honesty in public life and trust in politics”, broadcasters need to take into account Johnson’s long history of lying and misleading people.

Sent to the director general of the BBC and chief executives of the other major broadcasters, the letter said Johnson’s “wilful disregard for basic standards of decency are a threat to democracy”.

Among the untruths, top of the list was the false claim that Johnson’s Brexit deal has “passed” parliament when MPs simply voted at second reading to allow it to proceed for further scrutiny. Other claims include the idea that there will be “no checks between Northern Ireland and Great Britain”, when the government has admitted that businesses will have to fill in forms.

He said another lie was the claim that an extension to article 50 would cost

a £1bn a month, when money has to be paid to the EU anyway during the transition period and the costs of no-deal Brexit would be higher.

Watson also challenged Johnson’s claims to be embarking on the biggest hospital-building programme in a generation, when only six new hospitals are earmarked for reconfiguration and 34 will not get funding until after 2025.

A senior Conservative source said in response: “Tom Watson’s accusations led to a bungled probe into the claims of the fantasist Carl Beech, and went far beyond the reach of an MP. He should do the decent thing and put his days of letter-writing and smears behind him.”

Johnson will resume visits on Friday but is not expected to formally launch his campaign this week, while government business is still going on and parliament still sitting.

While ministers rush through legislation before parliament is dissolved, Labour criticised the government for failing to bring urgent plans to tackle the climate and environment emergency in time to meet the six-month deadline set by MPs earlier this year.

The climate and emergency motion, passed by parliament on the 1 May 2019, “calls on the Government to lay before the House within the next six months urgent proposals to restore the UK’s natural environment and to deliver a circular, zero-waste economy”.