They won’t buy you much, but two anti-Brexit fake banknotes claiming to be from the “Bank of Brexit lies” and declaring themselves to be “for the privileged few” have been deemed of such historical value they have been added to the collection of the British Museum.

The banknotes, produced by a pro-EU group in Bath, have been doctored to carry the faces of Boris Johnson and Jacob Rees-Mogg. The Johnson design, based on a £10 note, carries the slogan: “I promise not to pay the NHS the sum of £350m pounds”, while the “£50 guinea” Rees-Mogg version declares: “I promise to pay myself more than you”, and carries the fake motto: “Arrogantus Toffo Posterium”.

Tom Hockenhull, the museum’s curator of modern money, said the notes belonged in its collection because “we capture history. We collect things because they represent economic, social and political history, and so we want these in the collection.

“There’s a long tradition of making parody bank notes for the purposes of spreading a political message or advertising a particular viewpoint, and these fit into that genre.”

The notes were produced by Bath for Europe, which campaigns to stop Britain leaving the EU, and have already been distributed in their thousands at anti-Brexit rallies, said Dick Daniel, a founding member who designed the notes.

His original idea, he said, was to “play on the promises they made, the distortions and lies of the Brexit campaign, and to make something very visual”.

He had initially printed off a few hundred copies of the Johnson note, his first design, but after the notes proved popular, the group kept printing more. Daniel believes that up to 5,000 have now been handed out. The images are available without charge to download and use from the group’s website.

The British Museum’s move follows its acquisition earlier this year of a Banksy artwork depicting an equally fake banknote designed in 2004 and displaying an image of Princess Diana.

Those notes had to be withdrawn by the artist after he noticed people trying to spend them. The Johnson and Rees-Mogg notes, by contrast, resemble banknotes only on one side.

Quick guide What Vote Leave leaders really said about no-deal Brexit Show Hide Boris Johnson, prime minister Johnson told the Treasury select committee in March 2016: “Our relationship with the EU is already very well developed. It doesn’t seem to me to be very hard … to do a free trade deal very rapidly indeed.” Speaking at a Vote Leave event in March 2016, Johnson said: “I put it to you, all those who say that there would be barriers to trade with Europe if we were to do a Brexit, do you seriously believe that they would put up tariffs against UK produce of any kind, when they know how much they want to sell us their cake, their champagne, their cheese from France? It is totally and utterly absurd.” Johnson, then foreign secretary, told the House of Commons in July 2017:“There is no plan for no deal because we are going to get a great deal.” Dominic Raab, foreign secretary Two months before the June 2016 referendum vote, Raab told Andrew Neil on BBC Sunday Politics: “We’re very well placed, and mutual self-interest suggests we’d cut a very good deal and it’s certainly not in the European’s interests to erect trade barriers.” During an appearance on the BBC’s Daily Politics in April 2016, Raab added: “The idea that Britain would be apocalyptically off the cliff edge if we left the EU is silly.” Michael Gove, chancellor of the duchy of Lancaster In April 2016, Michael Gove said the UK would have the best of both worlds. “Outside the EU, we would still benefit from the free trade zone which stretches from Iceland to the Russian border,” he said. “But we wouldn’t have all the EU regulations which cost our economy £600m every week.” Liam Fox, former international trade secretary After the referendum, in July 2017, the then-international trade secretary Liam Fox said: “The free trade agreement that we will have to do with the European Union should be one of the easiest in human history. We are already beginning with zero tariffs, and we are already beginning at the point of maximal regulatory equivalence, as it is called. In other words, our rules and our laws are exactly the same.” Simon Murphy and Frances Perraudin

Hockenhull said the museum would gladly collect examples of pro-Brexit banknotes but he was not aware of any that had been produced. “I wonder if that is because the £350m figure is something they would rather forget rather than stick it on a banknote.

“This is the material culture of the politics of the last five years and the evidence suggests that this will have ramifications far beyond that, so I think these will be an important record of our time.”