Liberal senator Cory Bernardi has pulled out of a speaking engagement in England after his controversial comments about same-sex marriage.

Senator Bernardi resigned as parliamentary secretary to Opposition Leader Tony Abbott after an outcry over his speech linking gay marriage to the social acceptance of sex with animals.

He flew to London two days ago and had been due to address the European Young Conservative Freedom Summit this weekend at Oxford University.

But it is understood Senator Bernardi has decided not to go because of concerns his attendance would be a distraction.

The British Conservative Party had earlier moved to distance itself from the comments, which they said did not reflect the views of prime minister David Cameron.

Mr Abbott has described the comments as "ill-disciplined" and has accepted Senator Bernardi's resignation, saying they were views he did not share.

During a Tuesday night Senate debate, Senator Bernardi said the push for same-sex marriage was coming from "radicals" who were determined to overturn the social fabric of Australian society.

He questioned where the campaign would end, if society was prepared to redefine marriage based on the "latest criterion" that it should be allowed irrespective of gender.

"The next step, quite frankly, is having three people or four people that love each other being able to enter into a permanent union endorsed by society - or any other type of relationship," Senator Bernardi said.

"There are even some creepy people out there... [who] say it is OK to have consensual sexual relations between humans and animals.

"Will that be a future step? In the future will we say, 'These two creatures love each other and maybe they should be able to be joined in a union'.

"I think that these things are the next step."