Nigel Farage has backed the decision of Claridge’s hotel to ask a breastfeeding woman to cover up, saying that mothers should “perhaps sit in the corner” when they breastfeed.

The UK Independence party leader said he thought a lot of people felt uncomfortable about women breastfeeding in public and that breastfeeding mothers should be discreet – although it was not an issue he felt strongly about.

Speaking on LBC radio, he said: “I’m not particularly bothered about it, but I know a lot of people do feel very uncomfortable, and look, this is just a matter of common sense, isn’t it? I think that, given that some people feel very embarrassed by it, it isn’t too difficult to breastfeed a baby in a way that’s not openly ostentatious.

“Frankly, that’s up to Claridge’s, and I very much take the view that if you’re running an establishment you should have rules.”

When asked on LBC if women should be told to go to the toilet to breastfeed, Farage replied: “Or perhaps sit in the corner, or whatever it might be – that’s up to Claridge’s. It’s not an issue that I get terribly hung up about, but I know particularly people of the older generation feel awkward and embarrassed by it.”

Lou Burns (@Andysrelation) ...SO much more obvious with it than without! Such a shame I can never go back.... @ClaridgesHotel #breastfeeding pic.twitter.com/1DyNQUMYL4

Reacting to Farage’s position, No 10 said it was “totally unacceptable” for mothers to be made to feel uncomfortable about breastfeeding in public.

Prime minister David Cameron’s spokesman said: “It’s for Mr Farage to explain his views. The prime minister shares the view of the NHS which is that breastfeeding is completely natural and it’s totally unacceptable for anybody to be made to feel uncomfortable while breastfeeding in public.”

Labour’s shadow home secretary Yvette Cooper suggested Farage himself should sit in a corner.

Farage later attempted to clarify his comments, hitting out at “media fabrication” about his remarks, saying he had never said breastfeeding women should sit in a corner, but it was reasonable for an establishment to ask them to do that.

“Let me get this clear, as I said on the radio and as I repeat now, I personally have no problem with mothers breastfeeding wherever they want,” he said. “What I said was - and it is immensely frustrating that I have to explain this - is that if the establishment in question, in this case Claridge’s, wants to maintain rules about this stuff, then that is up to them, as it should be. I remarked that perhaps they might ask women to sit in a corner. Did I say I believe they should have to? No. Did I say I personally endorse this concept? No.

“We do however have to recognise that businesses have a responsibility to all of their customers, some of whom may well be made uncomfortable by public breastfeeding. It’s a two-way street: breastfeeding women should never be embarrassed by staff asking them to stop, and most mums will recognise the need to be discreet in certain, limited, circumstances. It just a question of good manners, and in this case, accurate journalism.”

Claridge’s sparked controversy earlier this week by asking Louise Burns, 35, to breastfeed under a cloth. Burns has told how she burst into tears after a waiter rushed up to her with a “ridiculous shroud” while she breastfed her 12-week-old daughter. She was apparently told that it was hotel policy for mothers to cover up while breastfeeding – something Claridge’s has since denied.

Downing Street initially made no comment about the incident on Tuesday before later saying it echoed the NHS guidance that women should be free to breastfeed in public.

But after the Ukip leader expressed his opinion, Cameron’s spokesman said: “It’s for Mr Farage to explain his views. The prime minister shares the view of the NHS which is that breastfeeding is completely natural and it’s totally unacceptable for anybody to be made to feel uncomfortable while breastfeeding in public.”

The London hotel has been condemned by the Liberal Democrat equalities minister, Jo Swinson, who said: “It’s depressing that when there are such well-documented benefits of breastfeeding, officious policies like this make new mums feel uncomfortable for doing nothing more than feeding their baby.

“Many babies don’t like feeding under a tent and mothers shouldn’t be forced to cover up, as if they are doing something illicit or wrong. Suggesting breastfeeding mothers should not be seen in society is archaic.”

In protest against the hotel’s decision, the campaign group Free to Feed is organising a “nurse-in” outside at 2pm on Saturday. The group described it is a peaceful demonstration in support of breastfeeding mothers. “Enough is enough. Claridge’s have had ample time to apologise for their mistake and rectify the situation by changing their ‘policy’, which states that they allow nursing mothers ‘as long as they are discreet’. Claridge’s seem to think that they are above the laws and legislation of this land,” a statement on the group’s website said.

At the time, a Claridge’s spokeswoman declined to discuss the incident, but said it did allow breastfeeding. “It is our policy never to talk about our guests,” she said.