A review of labelling of halal meat will be conducted if the industry fails to deliver more transparency within the next few months, Downing Street has said.
Much of the meat sold in British supermarkets and served in restaurants comes from animals slaughtered according to traditional Muslim rituals, but in many cases it is not labelled halal.
UK Independence Party leader Nigel Farage has said that labels should carry details of the method of slaughter, and said the UK would have to break with EU rules in order to ensure it is done.
But the Prime Minister has said that the issue is a matter between retailers and restaurants and their customers.
He told ITV West Country: "If you are going into a restaurant you assume that it is not halal meat unless you are told otherwise. Do we need a national labelling scheme? I would rather hope not. I would rather hope it could be dealt with by the restaurants and businesses.
"I think a lot of businesses and restaurants will probably change their practices and change their labelling.
We should start from the approach that the greater the transparency the better, and I hope we can achieve that transparency without necessarily having a full-on national labelling scheme.
A Downing Street spokeswoman said: "The Prime Minister thinks that British consumers want to see more transparency on this issue, that has arisen because people had not expected that so much meat was not labelled. He said, 'let's see if we can get some transparency and then we will review the situation in a few months' time'.
"British consumers are good at making clear their views on what they want and retailers, I'm sure, will look at working with consumers on this.
"We think, because of this debate that has happened, businesses and restaurants will look at consumers' interests in this area and the fact that they are expressing that they want more information. Let's see what happens over the next few months on that issue. The backstop is that we will review it, depending on what transparency there is."
Asked whether a review would look at the possibility of compulsory labelling, the spokeswoman said:
"When we get to a review, of course there are things we can look at, but we are not at that stage yet.
"Clearly there are some British consumers that want to understand more about the way the meat on their table has been slaughtered. What we are saying is that retailers need to work with consumers with this to come up with something that addresses consumer concerns. It's about providing more information for consumers."
Mr Farage told LBC 97.3 radio: "Over half of the meat sold in this country is halal. We have this debate about labelling, but it isn't the British Government, it isn't Defra that decides how we label food, it isn't the British Government that decides the rules for slaughtering animals. It's all done in Brussels.
"The EU looked at this in 2011.There was a big debate in the Parliament as to whether we should have much clearer food labelling and the European Parliament decided 'No, we are not going to do that'."
Mr Farage said he supported the right of the Jewish and Muslim communities to have meat prepared according to the rules of their religions.
But he added: "What I don't want is one particular form of meat production imposed upon everybody else.
"I think actually for once we should say we don't need Brussels to do this, we can sort it out for ourselves and let's have clear meat labelling. Who could possibly object to that?"