The charity which threatened to sue The The X Factor over the use of the name Rhythmix for its girl group has urged viewers to boycott voting for the acts – and give the money to them instead.

Brighton-based Rhythmix has claimed it incurred a legal bill of £8000 when the group – who have since changed their name to Little Mix – attempted to trademark the name.

And in a campaign on Twitter they have labelled #CowellMustPay they are asking viewers to text the charity instead of voting for the acts – so that they can get their money back.

The chief executive Mark Davyd said the charity had been forced into defending their name because otherwise they would not have been able to trade – even though they trademarked the name Rhythmix in 2006.

Although the trademark laws permit different types of trademark for different activities, Mr Davyd insisted that Syco entertainment tried to register in areas which would were similar to those of the charity.

“We have been forced into defending our trademark because Syco just would not listen to us,” he said.

“No-one from the show has been able to explain why they felt this was an appropriate thing to do to a charity. We are saying they forced a charity that for 12 years has quietly worked with vulnerable children to spend this money.

“We had a board meeting where we discussed the options and found that changing our name would have cost £20,000 and defending our trademark would cost £8,000-12,000.

“The money might not seem a lot, but £8,000 is 120 hours of work with a vulnerable person and it’s just three seconds of advertising revenue for the show.

Syco said earlier this week it had withdrawn the application to trademark the name and now considered the matter to be closed.