Saturday's wedding had been a closely guarded secret and it is understood that only a handful of people were aware of the preparations. Just 30 close friends and family attended the low-key ceremony.
Elizabeth Pierce, 68, said: "I don't understand how they got married here because he's been divorced ... and the Catholic church doesn't condone that, so once you're married that's it.
"I don't want to be the first, as it were, to cast the first stone but it doesn't look very well for us, his former past."
Regular attendees said that they did not hear any announcement of the marriage during services. However, wedding banns have not been a requirement in the Catholic church for a number of years.
Maria said that the priest had been unable to tell her why a divorcee was married in Westminster Cathedral. "It needs clarifying," she said.
Other members of the congregation supported the decision of Father Daniel Humpreys to marry them, saying that the Prime Minister was a free man.
A spokesman for Catholic Voices said: "The PM entered into a sacramental marriage yesterday. Many will ask: how is it that the Catholic Church, famous for its vigorous commitment to the permanence of marriage, should be witnessing the marriage of a twice-divorced PM who is publicly notorious for the opposite?
"What kind of message does that send? But Catholics have a right to the sacraments, and if they fulfil the requirements in law, and properly enter into them, no one can stop them exercising those rights."
Father Humphreys also baptised their son, Wilfred, in the chapel where they wed (the Lady Chapel) just six months ago.
The couple were both baptised Catholics, although the Prime Minister renounced his mother's Catholicism when he was confirmed in the Anglican faith while at Eton.
It is understood that the couple had been "under instruction" with the priest for "many months" before the ceremony.
A spokesman for Westminster Cathedral said: "The bride and groom are both parishioners of the Westminster Cathedral parish and baptised Catholics.
"All necessary steps were taken, in both church and civil law, and all formalities completed before the wedding.
"We wish them every happiness."