It would be easy for MPs in other parties to mock the Independent Group (TIG) of 11 MPs who have quit Labour and the Conservatives. Today they have announced the equivalent of their frontbench responsibilities: with so few hands on deck, some of their MPs will shadow three government departments.

And yet no one at Westminster is laughing at TIG: the two main parties are rightly worried about them. The new group has passed its first test – credibility. In week one, it had a successful launch. In week two, it enjoyed remarkable influence over Labour and the Tories. Without their breakaway, Jeremy Corbyn would probably not have backed a Final Say referendum or suspended his MP ally Chris Williamson for saying Labour has been “too apologetic” about antisemitism. Corbyn knew that failure to act on both fronts would drive more MPs into TIG’s awaiting arms. TIG’s very existence was a game-changer.

And the group undoubtedly added to the pressure on Theresa May applied by pro-EU cabinet ministers; other Tory MPs might have quit the party if she had not given the Commons a chance to block a no-deal exit on 29 March. Arguably, 11 MPs have been the catalyst for bigger changes on Brexit policy in two weeks than the remaining 639 MPs have won in two years.

Labour has most to fear. A survey for the Politico website found that 32 per cent of Labour voters say they are either likely or very likely to vote for a TIG candidate if they stood in their constituency. Younger voters and people living in London are most attracted to TIG.

Further recruits to the group from Labour’s ranks are likely when Brexit is finally resolved. Labour MPs are talking about forming “an independent wing” inside the party that might break away at a later stage, if its deputy leader Tom Watson cannot persuade Corbyn to change course. Watson, who is setting up a social democratic group of Labour MPs to discuss policy to try to keep them in the tent, holds the key to Labour’s future. There was a time when he would not do media interviews to avoid being asked: “Is Jeremy Corbyn fit to be prime minister?” – the £64,000 question for those Labour MPs wondering whether to jump ship.

Which MPs defected to form Change UK? Show all 12 1 /12 Which MPs defected to form Change UK? Which MPs defected to form Change UK? Change UK Details on the individual MPs are in the following photos Reuters Which MPs defected to form Change UK? Heidi Allen Anti-Brexit MP for South Cambridgeshire resigned from the Conservative party on February 20 PA Which MPs defected to form Change UK? Chuka Umunna MP for Streatham since 2010 and prominent People's Vote supporter PA Which MPs defected to form Change UK? Anna Soubry The prominent anti-Brexit MP for Broxtowe resigned from the Conservative party on February 20 PA Which MPs defected to form Change UK? Luciana Berger MP for Liverpool Wavertree since 2010, resigned from the Labour Party over bullying and anti-semitism PA Which MPs defected to form Change UK? Sarah Wollaston Anti-Brexit MP for Totnes resigned from the Conservative party on February 20 PA Which MPs defected to form Change UK? Joan Ryan MP for Enfield North resigned from the Labour party on February 19 citing its tolerance of a "culture of anti-Jewish racism" PA Which MPs defected to form Change UK? Ann Coffey MP for Stockport since 1992 Chris McAndrew / UK Parliament Which MPs defected to form Change UK? Gavin Shuker MP for Luton South since 2010 Getty Which MPs defected to form Change UK? Chris Leslie MP for Nottingham East since 2010 PA Which MPs defected to form Change UK? Mike Gapes MP for Ilford South since 1992 PA Which MPs defected to form Change UK? Angela Smith MP for Penistone and Stocksbridge since 2010

Watson is not holding back now. He told Radio 4’s Today programme on Thursday that Corbyn “could be” prime minister but Labour “could do without the antisemitism”. MPs not in the Corbyn fan club should rally behind Watson rather than argue about small differences over the right approach to the party’s crisis.

Ultimately, it will be Corbyn rather than Watson who determines how many Labour MPs eventually walk out. Team Corbyn will be tempted to ignore Watson; it has not forgiven him for his attempt to persuade Corbyn to stand down in 2016, a year before his remarkable general election performance. But Corbyn should listen to his deputy. If Corbyn fails to show real leadership in stamping out antisemitism, declines to give more centrist MPs shadow cabinet roles and influence on policy and allows 50 MPs to be deselected by their local parties, then TIG’s ranks will swell, and Labour’s election prospects diminish. Corbyn’s handling of Brexit will also be important. Although he is edging towards backing a public vote in return for allowing May’s deal to pass the Commons, he will be happy if anti-referendum Labour MPs defeat him. As one MP put it: “He will go into the division lobby with his fingers crossed behind his back.”

So it is quite possible to see circumstances in which another 50 to 70 Labour MPs join the group, whatever they say about “staying to fight” now.

TIG is showing that small fish can have a big influence in the political pond. You don’t necessarily need vast numbers of MPs; the spectre of Ukip spooked David Cameron into calling his unnecessary, ill-fated referendum. The SDP forced Old Labour to become New Labour.

When TIG becomes a fully fledged party, it will find it very hard to break through under our archaic first-past-the-post system. And for now, when the new group has no policies, it can be all things to all people; that will not last. However, politics is much more volatile and fluid than in the SDP’s day, so a breakthrough is not impossible.