The Independent Group (TIG) of breakaway MPs want to form a rival to the Tories and Labour to fight the next general election.
A delegation of the group’s MPs held talks with the Electoral Commission about becoming a fully-fledged party but “no specific timeframe” was set for the process.
Group spokesman Chuka Umunna said the goal was to be ready to field candidates in the next general election, whenever that is held.
The next scheduled contest is not until 2022, but the turmoil in Westminster politics means that an earlier election remains a distinct possibility.
Mr Umunna said the group had been “overwhelmed by the tens of thousands of people who have signed up to our website, who have shown support for what we are doing”.
He added: “We aren’t a political party but quite clearly there is an appetite for a new one, so we are here to discuss with them what that involves.”
Mr Umunna was joined by former Labour MPs Gavin Shuker, Ann Coffey and Chris Leslie along with former Tory Heidi Allen at the Electoral Commission headquarters in London.
He played down the prospect of rushing through the process in order to contest May’s local elections.
“One step at a time. We have just been given a lot of information, we want to make sure we do things in the right way.
“In terms of decisions on local elections or any other elections in the immediate next few months we will make decisions about that.
“But we are clear that when a general election comes, people want an alternative.
“We have been advised that the only way that you can actually deliver that is by being a registered political party so you can be on the ballot paper. That is our goal.”
The Electoral Commission meeting comes just over a fortnight after Mr Umunna, Ms Coffey, Mr Leslie, Mr Shuker, Luciana Berger, Angela Smith and Mike Gapes resigned from Labour, signalling the biggest shake-up of Westminster politics for a generation.
They were soon followed by former Labour colleague Joan Ryan and ex-Tory recruits Ms Allen, Anna Soubry and Sarah Wollaston.
Registering with the commission would allow TIG to field candidates in elections but would also require it to comply with strict rules on funding.
The group has promised to comply with party funding rules even before it formally registers with the watchdog.
Mr Umunna said he wanted the group to offer the “politics of the future” as an alternative to the “rotten” culture of the established Westminster parties.
“In the coming weeks and months we want to ensure that we properly involve everyone in the country who wants to see that alternative come into being,” he said
“We will be launching a ‘change politics project’ which we will be taking all over the country to include people in the process.”