Global Counsel warned there will be “a significant number of redundancies being made by the administrators when they take control of the company” on Friday.
The lobbying firm was set up by Lord Mandelson and Wegg-Prosser after Labour lost the 2010 general election.
It became a highly influential lobbying firm in Westminster, advising high-profile clients such as Shell, TikTok and Barclays.
The company employs more than 100 people and has offices in Berlin, Brussels, Singapore, Washington DC and Doha.
However, its future was thrown into question following the publication of documents from the Epstein files, which cast light on Lord Mandelson’s links with the disgraced financier.
In a statement on Thursday, Global Counsel said “many clients” had remained loyal to the firm in recent weeks.
But it added: “The continuing maelstrom of political and media attention surrounding Peter Mandelson has made it challenging to continue with the business in its current form.
“The administrators-in-waiting have already indicated that, in the unlikely event that any ongoing servicing of clients is viable, this will be on a limited basis only.”
The files also contained mentions of a meeting between Wegg-Prosser and Epstein in 2010, two years after the latter’s conviction for soliciting prostitution and soliciting a minor.
Epstein died in New York in 2019, while awaiting trial on sex trafficking charges.
Lord Mandelson is credited as one of the key architects of the New Labour movement, which came to power with Tony Blair’s election victory in 1997.
He served in several ministerial posts under Blair and Gordon Brown, as well as being European commissioner for trade from 2004-2008.
He was appointed ambassador to the US in December 2024, but was fired in September after the extent of his relationship with Epstein became clear.
Earlier this month, two properties linked to Lord Mandelson were searched by police following allegations of misconduct in public office.
Lord Mandelson has been contacted for comment but has not responded. The BBC understands his position is that he has not acted in any way criminally and that he was not motivated by financial gain.