The Fundraising Standards Board (FRSB) said it is “deeply concerned” about the claims made and said it will investigate.
Other charities also said they will look into the issues raised following an investigation by a Sunday newspaper which highlighted the techniques used by call centre Listen Ltd.
Tim Hunter, Oxfam’s director of fundraising, said: “We take the allegations contained in the article very seriously and have suspended all operations with both Listen Ltd and Street Academy, pending a thorough investigation.
“Oxfam carries out regular quality checks of fundraising calls on our behalf and insists on high standards of training and monitoring.”
Listen says it is an established fundraiser, while Street Academy aims to raise the standards of street fundraising and is part of housing charity Shelter.
In a statement, Listen said: “Listen, an established and multi-award winning fundraiser, which raised over £40 million for UK charities last year, provides training to all employees in accordance with the requirements of the sector’s regulators and is looking into the claims.”
Campbell Robb, chief executive of homeless charity Shelter, said: “Street fundraising remains an important income stream for the charity sector. Shelter relies on public support and funding for the majority of our activity, and without this we simply couldn’t continue to be there for everyone who needs us.
“We take any accusation of bad practice amongst street fundraisers employed by the Street Academy seriously, and undertake regular mystery shopping to make sure that they adhere to our strict code of practice and that of the Institute of Fundraising at all times.”
Nick Georgiadis, head of direct giving at Cancer Research UK, said the charity was “deeply disappointed” to hear of the allegations.
He added: “Cancer Research UK relies on people’s generosity to fund our life-saving work. Our research has fuelled the progress that has seen survival rates for cancer in the UK double in the last 40 years. In the 1970s just a quarter of people survived. Today that figure is half.
“At Cancer Research UK, we are grateful for every donation we receive and would never want anyone who gives us their support to feel pressured in any way. We’re deeply disappointed to hear these allegations against Listen Limited and we will be investigating this matter urgently.”
A Unicef UK spokesman said they expect “high standards” from the agencies who raise money for them and said they are investigating.
The FRSB said: “The FRSB will investigate these claims to establish whether any breach of fundraising standards has taken place.”
In a statement the RSPCA said: “All of our fundraising activity is conducted in line with the Institute of Fundraising’s (IoF) code of practice and we are also an active member of the Fundraising Standards Board (FRSB).
“Both the IoF and FRSB are conducting reviews of current practice within charity fundraising.
“We will be fully involved in these reviews and follow any resulting recommendations.”
The claims have been made just a few weeks after one of Britain’s oldest and longest-serving poppy sellers was found dead after receiving hundreds of letters a month from charities.
Olive Cooke, 92, died from from multiple injuries after jumping into Avon Gorge on 6 May. Her family have insisted that – while the letters and phone calls were intrusive and a nuisance – the charities were not to blame for Mrs Cooke’s death.