More than 40 Conservative MPs will informally launch a new grouping this week – called 2020 Conservatives – to help David Cameron in his struggles with the Right of the Parliamentary party.

But 2020 Conservatives, as the name implies, also has the aim of taking the Cameron modernisation project beyond the period of Cameron’s leadership.

 The group will be drawing up policies for the election after next – due under the new rules in 2020 – by which time, it is widely assumed, Cameron will have stepped down as Conservative leader.

Conservatives 2020 will is being organised by Greg Barker, the junior DECC minister, who was one of Cameron’s earliest supporter when he first stood for the Tory leadership in 2005.

Other MPs involved include the Development Secretary Andrew Mitchell (who actually ran David Davis’s campaign in 2005), Hugo Swire (another early Cameroon), and many MPs from the 2010 intake, including Claire Perry and George Freeman.

2020 Conservatives has been established because many MPs on the Conservative Centre Left fear that the Right has made to much of the running since the Coalition came to power, with its various groups and dining clubs at Westminster.

They fear that the Right has been especially effective in recruiting members of the 2010 intake, whilst the more centrist side of the party has been badly organised.

They think that Cameron has often been isolated in arguments with his backbenchers, with too little support from Tory MPs in the centre and left of the parliamentary party.

2020 Conservatives claims to have obtained good funding. It aims in due course to work beyond just the parliamentary party, with a website and regular publications.

It may eventually try to play a role in helping the selection of like-minded parliamentary candidates.

Above this is a wider aim. Cameroons observe with some anxiety what happened to Tony Blair.

They note that the Blairites did little to ensure, while Blair was Prime Minister, that the Blair Project continued after he left office, that the revolution was permanent. Instead, under Gordon Brown and Ed Miliband, it largely died.

The aim is to ensure that the Cameron revolution survives, and develops, long after he steps down as Tory leader.

Andrew Mitchell told me tonight that the group was the embodiment of “modern, compassionate Conservatism” (which just so happens to be the name of David Cameron’s new pamphlet).

Other names I have discovered are involved are Helen Grant, Matt Hancock and Jesse Norman (the latter two both former Osborne aides, like Claire Perry).

A couple of the MPs involved were upset when I described the grouping to them as Centre Left. One said “progressive” was a better word. One MP said that 2020 Conservatives hoped to have a big web presence, and to counter the influence of ConservativeHome.com