Sir Keir Starmer believes that Lord Mandelson should no longer be a member of the House of Lords or use his title over his links to Jeffrey Epstein.
Our political correspondent Mhari Aurora says the process of removing his peerage wold not be easy.
"Peers can obviously publicly resign themselves, which is realistically what the government is going to be hoping for," she says.
"But if not, there would need to be legislation passed in order to actually remove peerages from members of the House of Lords, and from what we can understand, that would be quite a long and difficult and arduous process.
"Perhaps the House of Lords themselves might block that legislation."
Watch Aurora's analysis...