In the messages, Mr Hancock and his aide Allan Nixon discussed refusing a learning disability hub in Bury, Greater Manchester, that Bury North MP James Daly was campaigning for if he did not back the Government in the crunch vote.
Mr Nixon said: “I think we need to dangle our top asks over some of these 2019 intake MPs who are going off the boil this coming week.
“Thoughts on me suggesting to Chief’s spads that they give us a list of the 2019 intakes thinking of rebellion.
“E.g. James wants his Learning Disability Hub in Bury – whips call him up and say Health team want to work with him to deliver this but that’ll be off the table if he rebels.
“These guys’ re-election hinges on us in a lot of instances, and we know what they want.
“We should seriously consider using it IMO.”
Mr Hancock replied: “Yes 100 percent.”
Mr Daly told The Telegraph he was “appalled” and “disgusted” that the disability hub had been considered as a way of forcing him to vote for the Government.
But Mr Daly added he was surprised at the threat as the centre “never got dangled in the first place”.
He said: “They were never proposing to give it to me. I still don’t have it. Even though I have repeatedly campaigned for it, Hancock never showed the slightest bit of interest in supporting it.”
In the vote, 55 Conservative MPs voted against the tier system meaning Boris Johnson had to rely on Labour abstaining to get the measures through.
The exchange is part of more than 100,000 of the former health secretary’s leaked WhatsApp messages.
Mr Hancock gave the messages to journalist Isabel Oakeshott as they collaborated on his memoirs, but she subsequently handed them to the Telegraph which has sparked a flurry of stories based on the correspondence.
A spokesperson for Mr Hancock said: “As we’ve repeatedly seen this last week, it is completely wrong to take this entirely partial account and write it up as fact.
Read More: Matt Hancock discussed plan to block centre for disabled children if MP opposed lockdown