A leader may not be elected to the newly formed Independent Group of MPs until the end of the year when it hopes to have become a political party.

The 11 former Labour and Conservative MPs’ first meeting in Westminster selected Gavin Shuker to act as its convener and organise future meetings but while there were initial conversations about roles and responsibilities, there was no serious discussion as to who might become leader.

Chuka Umunna, a former Labour frontbencher, has been widely tipped for the role but friends of Heidi Allen, a former Conservative, have been pressing her to put her name forward when the election process begins.

Speaking about the leadership, Allen said immediately after the meeting: “You’ll be gagging to learn we’ve started talking about the other jobs and roles and responsibilities.” Anna Soubry, another group member, added: “The most important thing this week is Brexit.”

Over the weekend, Umunna sought to put himself forward, saying: “I’m clear I want to play the biggest role in this group.” It appears, however, that his immediate ambition has been rebuffed, at least temporarily.

Others have suggested that Luciana Berger, the MP for Liverpool Wavertree, could also take the leading role, although because the group has no grassroots members yet, it is not clear how a leader could be legitimately elected.

Insiders said the intention was gradually to turn the Independent Group (TIG) into a political party, and there would be “much more clarity about that by the end of the year” – although some specialist spokesperson roles could be assigned much quicker.

Donations are understood to be coming “in the hundreds of thousands”, largely from individuals giving fairly small sums. The money is likely to be spent on support staff initially.

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Although the group is not required to, it intends to follow Electoral Commission rules and make regular disclosures, reporting the identity of donors who supply more than £7,500 in one year. This follows accusations it could circumvent existing rules because it is not registered as a political party.

TIG will not operate a whip, partly to resolve differences of opinion over other policy areas, although the 11 MPs are strongly aligned in opposing Brexit and supporting a second referendum.

The first meeting also agreed that any MPs wishing to join TIG will have to apply. In theory, this would allow its members to block MPs who left Labour amid unresolved harassment claims from joining, including John Woodcock or Ivan Lewis.

No further defections are anticipated imminently, although the group hopes that the forthcoming parliamentary battles over Brexit could see other MPs coming forward.

TIG has no immediate plans to contest any parliamentary byelections or the council elections due in May. Its 11 members have repeatedly ruled out resigning as MPs and triggering a byelection until its organisation develops.

Jo Swinson, the Liberal Democrat deputy leader, said her party needed “to be working together with the Independent Group MPs but we need to find a 2019 way of doing that and I’m open-minded about how that looks”.

But despite Lib Dem enthusiasm, TIG MPs said they wanted Lib Dem MPs to quit their party and join them. They argued that the Lib Dem brand has been tarnished by the period when the party under Nick Clegg went into coalition government with David Cameron’s Conservatives.