The newspaper published allegations based on an undercover recording and text messages to and from the MP, who is married to a woman. It said he used male prostitutes, offered to buy cocaine for one of them and discussed using the legal drug poppers.
The fact that as chair of the Home Affairs Committee, Vaz has had a key role in influencing policy around prostitution and drug laws, has attracted particular comment as most other newspapers carry the story on their front page today.
Vaz has said he will stand down from the post tomorrow.
Vaz said it was "deeply disturbing" that a newspaper would use the undercover tactics involved in getting the story, and said: "I have referred these allegations to my solicitor Mark Stephens of Howard Kennedy who will consider them carefully and advise me accordingly." He also said he was "genuinely sorry for the hurt and distress" his actions had caused to his family and others.
Former Labour MP and now managing partner of Connect Communications Andy Sawford said that the legal element in the response should not have been so firm or prominent. "Rather than issuing robust statements about getting the lawyers involved, I think the best thing now would be a simple statement of contrition followed by a period of silence," he said.
Sawford went on to say: "The Mirror will have calculated that the public's dislike of their underhand methods in making a secret recording, will be secondary to their dislike at the appearance of double standards. If these allegations are true, and Keith doesn't seem to be contesting that, I doubt that he will be able to fully recover his reputation and his position."
Alex Deane, the UK head of public affairs at FTI Consulting, added: "In PR terms he would be well advised to keep his head down for a while now - no matter how tempting it may be to defend himself with real or imagined points - for the simple reason that he presently has little idea what else the media has on him - relating to this or otherwise."
Shimon Cohen, founder of The PR Office, said: "Rather than seek to shift the blame for one's personal failings, Vaz should be showing humility and expressing remorse. Mr Vaz, while in a hole, should seek PR advice and stop digging."
Jonathan Hemus, founder of Insignia Communications, said: "The challenge for Keith Vaz is to emerge from this incident with sufficient credibility and trust to continue as chairman of the Home Affairs Select Committee. Crucial to this will be his ability to either discredit the allegations or position them as a purely private matter unrelated to his public life. His initial response indicates that he is focusing on the former strategy.
"As many organisations and individuals have found over the years, a crisis brings with it an intense media spotlight and Mr Vaz’s previous behaviour will now come under intense scrutiny. To salvage his reputation, he badly needs credible third parties to step forward and speak on his behalf and, of course, to hope that there are no further damaging allegations to come."
However, Gill Morris, founder of the public affairs agency DevoConnect, who has worked with Vaz and various other Labour MPs, said she would not bet against Vaz bouncing back.
She said: "It is important to remember that Keith Vaz is a very clever man and legal brain. He has had trials and tribulations before and has always bounced back and just maybe he can live to fight another day."
Labour leader Jeremy Corbyn also expressed a degree of sympathy for Vaz, saying that the allegations appeared to be "a private matter", while fellow Labour MP Simon Danczuk pointed out on Twitter that Vaz did not seem to have broken any laws.