Out of 39 mental health trusts that provided figures for their crisis teams, 27 had seen their workload increase - 70%.
And some had seen referrals rise by as much as 60% - but without a comparable rise in funding.
NHS England said an extra Â£400m would be spent on crisis resolution teams.
BBC Radio 5 live contacted all 54 mental health trusts who run crisis teams in England.
One of them, East London NHS Foundation Trust, revealed its crisis team had seen referrals increase from 7,057 to 11,368 last year, a 60% rise in demand.
Camillo Parra-Braun's wife, Mariana, died by suicide at the age of 32 in October last year.
Mr Parra-Braun had contacted the City and Hackney mental health home-visit team twice that day because of concerns about his wife's deteriorating mental health.
He was told they were unlikely to be able to see them before 17:00 and more likely nearer 19:00.
If he had urgent concerns, they said, he should contact the police.
But help came too late for Mariana.
Mr Parra-Braun said: "And after I learned of her death, my phone rang, and it was the crisis team, and they told me they would be arriving around 19:00."
A statement from East London NHS Foundation Trust said: "We would like to extend our condolences to the family and friends of Mariana Pinto and everyone who has been affected by this tragic event.
"Following the incident, the trust subsequently carried out a thorough review into the care and treatment of Mariana Pinto which involved meeting with family to discuss the case and establish their concerns.
"The patient's family were also given the opportunity to contribute to the report."
In 2014, a report for NHS England acknowledged the system was "stacked against" mental health.
And last year a further report for NHS England said the majority of crisis teams "are not currently sufficiently resourced to operate 24/7, with caseloads above levels that allow teams to fulfil their core functions".
Staff working within teams were too scared to speak publicly, but one person told BBC News anonymously: "Our referrals are increasing all the time.
"And no, we do not have enough money to deal with [the] increase in referrals.
"The CCG [Clinical Commissioning Group, which allocates NHS funding locally] simply does not have any money."
An NHS England representative said: "NHS investment in mental health services is rising faster than for other services and this includes an additional Â£400m invested in crisis-resolution home-treatment teams from this year so that all areas are able to offer 24/7 emergency care to those who need it."
In January, the government published its response to a taskforce report into the state of mental health services.
It said that it would accept the recommendations in full and would deliver "additional investment of Â£1bn a year by 2020-21 to improve mental health services".
"As the prime minister has said, it is this government's ambition to tackle the burning injustices that persist in our society, including the inequalities caused by poor mental health and the continued inability of many people to get the mental health treatment they need," it said.
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Rehoboth Baptist Chapel, next to the Regent Circus development in Swindon, was closed in January 2014 because of damage to its ceiling and walls.
Repairs by developer ISG had been expected to start two months ago.
The BBC has asked ISG for a comment but the company has not responded.
The chapel and people living near the Regent Circus complex, which opened fully in February, said they had been reassured by ISG at a public meeting in March 2014 that the damage would be "put right".
Tracy White, from residents group Back Garden, said the company had offered nearby residents a property survey and had also agreed to write to all those affected.
She said when she had contacted ISG to confirm whether "the letter was actually circulated to residents" she had received no reply.
Ms White said: "At that meeting, ISG's director made a public commitment to rectify any problems that the surveys identified.
"We know that there are residents on Cross Street whose properties back on to the development that have no access to their garages and back alley, which has remained closed off with fencing for nearly two years.
"We were also led to believe repair work would begin in February and March, and that concrete underpinning would start in April.
"Again, nothing has happened with this work."
Rehoboth Baptist Chapel has been hiring nearby St Mary's church for its congregation since the chapel closed last year.
Services for people who are suicidal or self-harming are facing unprecedented demand in England, a BBC Radio 5 live investigation has found.
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A chapel which closed more than a year ago when cracks appeared during the construction of a nearby retail complex is still awaiting repairs by the developer.