A pledge to spend the “dividend” secured by staying in the European Union on nationwide regeneration is being drawn up by senior Remain strategists ahead of a possible second referendum. In anticipation of a fresh poll, they are developing plans for a grassroots campaign that will operate without a traditional figurehead.

Eyecatching promises to spend billions on “left-behind” communities, the NHS and areas affected by high levels of migration are among the ideas being developed by campaigners keen on avoiding the mistakes of the much-criticised 2016 operation.

With Theresa May under pressure from her cabinet to delay a vote on her Brexit deal, figures on both sides of the debate are now planning how they could win a second public vote should a referendum emerge as the only way to break the political deadlock. Leave donors and pro-Brexit MPs are already said to have held talks about how to fight for a hard Brexit.

The Remain camp is desperate not to repeat the mistakes of the last campaign to keep Britain in the EU, which was labelled “Project Fear” for its alarmist predictions about the consequences of leaving the bloc. “There needs to be a positive vision and a message that things won’t just stay the same should the country back Remain,” said one senior strategist.

There are already plans to have no designated leader and instead rely on the grassroots movement for a second vote that has developed since 2016. This would avoid relying on figures from the first referendum who were regarded as representing the establishment and an unsatisfactory status quo. A slogan is also being developed that will make it clear that a Remain vote would not mean “no change”.

Attention has already turned to how the financial dividend from reversing the Brexit vote would be used. According to the Institute for Fiscal Studies, May’s deal would have a negative fiscal impact of some 1.8% of GDP in the long term, which campaigners say equates to about £36bn.

Remain figures from Labour, the Conservatives and the minor parties are already backing three ideas drawn up by people working with the pro-Europe Common Ground thinktank, including former Tory minister David Willetts. They are designed to address “the underlying problems that led many people to vote for Brexit in the first place”.

The first is a “jumpstart fund” for parts of the country starved of investment compared with London and other big cities. The money could be spent on public infrastructure, housing, local transport, skills or business development. Crucially, there is support for local communities to be given a say in how the money is spent.

Second, a further cash injection for the NHS, above the 3.4% annual increases pledged by May, is seen as key. Campaigners believe it would alleviate concerns about the health service and highlight the misleading Vote Leave claim that money sent to Brussels could be diverted to the NHS should Britain vote for Brexit.

Third, ideas are circulating about spending the net tax take from EU nationals in the UK on underlying issues that fuelled the Brexit vote. Research for the government’s Migration Advisory Committee put EU nationals’ contribution at £4.7bn. One suggestion is a “Migration and Communities Fund” for areas affected by significant migration of all kinds. However, there are already splits over the details, with some campaigners wanting the money to be used more generally to help poorer communities. Yesterday, Labour MP Anna Turley and other People’s Vote campaigners backed the idea of spending it on a globalisation fund for communities that have been “left out and left behind”.

Senior figures are wary of imitating the Leave campaign’s tactic of making promises that would not or could not be fulfilled. There is also some nervousness among Tory supporters of a second referendum about making wild spending pledges, though most agree that some guarantees about boosted local services will have to form part of the offer.

The People’s Vote and Best for Britain campaigns, which both back a second referendum, are running events and rallies this weekend to boost support. A newly developed app makes it easy for the public to lobby their MP for another vote. Strategists claim to have a network of some 30,000 activists across the country ready for a new campaign.

Leave campaigners are also gearing up for a new poll, though several believe a general election is more likely. Richard Tice, of Leave Means Leave, has already said he has begun planning a campaign. Meanwhile, former Tory election supremo Lynton Crosby has denied his company is formally involved in campaigns for a hard Brexit. There have been reports that an associate was working with Tory MPs on opposing May’s Brexit plans, including discussions about a new referendum campaign.