A new law to ban the use of wild animals in circuses is being repeatedly blocked by a trio of Tory backbenchers, despite the personal support of David Cameron, the government, Labour and over 90% of the British public.

The bill was blocked for the seventh time on Friday afternoon, a move its supporters called a “travesty” and an “outrage”. Dozens of lions, tigers, zebras and camels are still used in travelling circuses and in 2012 the government pledged to outlaw what Cameron called the “outdated practice”. But despite publishing the draft law in 2013, it has since failed to pass it.

Former environment minister Jim Fitzpatrick, a Labour MP, took the government’s bill and presented it as a private members bill, with support from MPs from all main parties. But it has been repeatedly blocked by circus-supporter Andrew Rosindell, along with Christopher Chope and Philip Davies, all Conservative MPs.

“It is very much a matter of a tiny number of Tory backwoodsmen preventing this from happening,” Fitzpatrick told the Guardian. “It is frustrating, but we are keeping the issue alive - it won’t go away.”

“The days of transporting wild animals in the back of lorries around towns and cities to show them off to people are long gone,” he said, noting that many nations, from Bosnia to Bolivia, already have bans and that safari parks and zoos provided alternatives. “We think Britain should join the 21st century.”

“It is a travesty that the actions of just three MPs are preventing legislation to end animal suffering from being passed,” said Jan Creamer, president of Animal Defenders International. In April, Cameron told ADI: “Yes, we are going to do it.”

A spokeswoman for the Department of Environment, Food and Rural Affairs (Defra) said the government bill would be passed “when parliamentary time allows”. However, the current parliamentary programme has the smallest number of bills for 20 years. Fitzpatrick said there clearly was time and he had “no idea” why ministers will not fulfil their pledge.

The British Veterinary Association backs the ban, stating: “The welfare needs of wild animals cannot be met within a travelling circus, in terms of housing or being able to express normal behaviour.” The RSPCA said: “Cramped and bare temporary housing, forced training and performance, loud noises and crowds of people are often unavoidable realities for the animals.”

But Rosindell, who has blocked the bill twice said: “The circus is a Great British institution, which has proved that it has the high standards of welfare which are rightly expected of it, and I strongly believe that it deserves to be defended against the propaganda and exaggerations.”

He added: “None have been taken from their natural habitat; all are from several generations of animals born in captivity. I believe it would be much more cruel to remove them from the life they have always known in living and performing with their loving owners in the environment they are accustomed to.”

Neither Chope, who has blocked the law four times, or Davies responded to requests for comment. Chope said in the Commons that the government should present the bill, not a backbencher. Davies, who blocked the bill in October, said he wanted to clear the way for a backbench bill on an EU referendum, which has since been killed off.

Creamer said: “By blocking the bill they are defying not only the wishes of their own party and their constituents, but also the British public and Parliament. There is also clearly time to pass a ban and the government needs to act now.” A 2010 government consultation found 94% of the British public supported a ban on wild animal acts.

Maria Eagle, Labour’s shadow environment secretary, said: “The British public will be outraged that, when given the opportunity, a determined group of Tories have repeatedly dug their heels in. The next Labour government will ban wild animals in circuses.”

Fitzpatrick said: “I think a ban on wild animals will come in sooner rather than later, but I have severe reservations about whether we get it in before the election next May.”