A statement issued by the charity on Friday afternoon said that, in the face of "significant changes and prevailing economic conditions", it has "not been possible to sustain the organisation".
Some of the organisation's functions will transfer to children's charity Coram, resulting in the creation of a new entity, CoramBAAF Adoption & Fostering Academy.
CYP Now has learned that out of 140 staff, 55 staff will transfer to CoramBAAF.
Coram said a further 29 staff are currently being "retained" by administrators at BAAF's offices in Scotland, Wales and Northern Ireland until a final decision is made on what will happen to those operations.
That means as many as 56 have been left without a job, a total that could rise as high as 85 if those 29 staff in Scotland, Wales and Northern Ireland are not kept on permanently.
One former member of staff took to Twitter to say that staff were told last Monday that a 90-day consultation would be launched and the sudden closure came as a shock.
She claimed that a statement on the BAAF website, which said that staff are "being supported" was not true. "That is a lie, no support offered," she said.
"We've also been locked out of our emails. Gets worse and worse."
Another member of staff got in touch with CYP Now to say that they had not received any redundancy or notice pay.
"The only support was a photocopied sheet from the administrators with a link to the govt website. Chief Exec and trustees have not helped at all."
Andy Leary-May is chief executive of Adoption Link, which works on behalf of local authorities to match children with registered adopters.
He said the fact that Coram, which provides services as a voluntary adoption agency, is now responsible for running the independent review mechanism - which reviews the suitability of prospective adopters - throws up a conflict of interest issue.
"BAAF was almost uniquely independent," he said. "Some of its vital services were provided on behalf of government, and stakeholders now deserve to see some consultation about how these functions should continue.
"The absence of any warning or transition planning was shocking for a charity like BAAF.”
Anthony Douglas, former chair of trustees at BAAF, and currently chief executive at Cafcass declined to comment.
A spokeswoman for Coram said: "It is always sad when an organisation goes into administration as choices are limited and invariably hard choices have to be made.
"Coram has been able to preserve the jobs of 55 former BAAF staff but, sadly there is a number who were made redundant.
"While we are pleased that we were able to step in and offer assistance, that of course does not mean that we do not all feel saddened by the loss of an organisation which was such a foundation stone in our community."