I was almost 22 in March 1981 when the SDP gang of four (as we called them in those days – an echo of the post-Mao junta ruling China) split from the Labour party. I had only just joined the Liberal party.

Within months, there were nearly 20 liaison committees between the SDP and the Liberal party in Oxfordshire, where I was living. I spent my 20s sitting on them and delivering leaflets – rather than drinking and partying as I had meant to.

The delivering at least got me exercising; the committees were a staggering waste of time. So it is worth remembering now that the merged party that resulted is suddenly in a similar position as they contend with the new Independent Group in parliament.

It’s a difficult paradox for the Lib Dems. On the one hand, this is a tribute to the kind of politics they espouse; on the other, it could so easily cramp their style and crowd them out. They have to embrace it somehow, without ending up in the bureaucratic nightmare that swallowed my 20s.

So this is what I believe Vince Cable should do. As soon as possible, the Lib Dems should join the Independent Group in parliament. I suggest this partly for the good of the independents. Joining the 11 Lib Dems (plus Stephen Lloyd, who resigned the whip recently, but who would surely then follow suit) would double their size and give them momentum. The new group would then be almost two-thirds of the way to becoming the third largest party (currently the SNP with 35 seats), and closer to the public funding attached for policymaking.

I am not suggesting that there should cease to be a Lib Dem group. I see no reason why they should not be a party in their own right, as the Co-operative party manages to be within Labour.

Some would object that the Lib Dems would lose their distinctiveness inside this passionate but slightly indistinct grouping. This loss of individuality was certainly a factor for the old Liberals in 1981, who had just voted against economic growth “as conventionally measured” and had been the only MPs to vote against the white elephant of a nuclear reprocessing plant at Windscale/Sellafield. But the truth is – though it breaks my heart to say so – the Lib Dems these days have no obvious distinctiveness to lose, and must face up to that.

‘I must admit my heart sank when the Independent Group’s Anna Soubry put “sound finance” top of her policy wish list last week.’ Photograph: Mark Thomas/REX/Shutterstock

If Brexit has divided the big parties, it has also separated the Lib Dems from their Brexit-voting supporters in the west country and Celtic fringes. It has hollowed out their message so thoroughly that only the cognoscenti can discern one.

Part of the problem in the 1980s was that those individuals who chose to join the SDP tended to be those most suspicious of the grassroots – and who clung most closely to parliamentary pomp. They were therefore least able to discern a new kind of politics in practice. Nobody is saying the current group is like that, so far. But they may turn out to be Westminster people and, like the old SDP, not easy to portray as insurgents.

It may also become more difficult to join the independents as they become more formal. Nobody would expect any kind of formal agreement now not to stand in each other’s constituencies at the general election, but it won’t be long before they will insist. It may not be within Cable’s power to provide this, but it needs to be faced urgently whether he joins the independents or not.

What the Lib Dems would bring to the new group is depth, because they have history – 160 years of it, in fact. And this might be a useful addition to a new group that has no depth at all.

I must admit my heart sank when the Independent Group’s Anna Soubry put “sound finance” top of her policy wishlist last week. It depends what she meant, of course. If she meant it has to work for everyone, then fair enough. But the word “sound” tends to mean “conventional”, which is about the last thing we want. A new kind of politics that fails to provide us with a new kind of economics – effective for the people and the planet, and tackling the threat to our prosperity from emerging monopolies – is really not worth the effort.

Very quietly, the Lib Dems have been thinking about these issues, and they can help the combined group – if they can all raise their heads from Brexit for a short period.

As a veteran of 1981, I dare not mention “breaking the mould” – but the gang of 11 is right now the best hope for breaking the stranglehold of right and left conservatism in Westminster. That’s why the Lib Dems must join now, not later.

• David Boyle is policy director of the radical centre thinktank Radix