Downing Street has agreed to a partial climbdown on reforms of trade unions amid warnings that the EU remain campaign needs to keep their members on side for the 23 June referendum.

After a protracted battle over the trade union bill, the government proposed delaying changes to political funding and agreed to a trial of e-voting for strike ballots.

Ministers will still force trade unionists to opt into their organisation’s political fund, rather than subscribing automatically, in a move that Labour has warned could cost the party up to £8m a year.

However, amendments tabled by the government on Tuesday afternoon would mean the changes now come into force after a longer transitional period of 12 months rather than three.

Ministers also agreed to pilot e-voting for strike ballots – a change suggested by the House of Lords.

It comes after a previous climbdown over plans to make all civil servants and staff in the wider public sector who belong to a union switch to direct debits or make other arrangements to pay their fees, rather than having them deducted from their salaries.

The government tabled the changes before the trade union bill returns to the House of Commons on Wednesday and its likely return to the House of Lords next week.

David Cameron’s official spokeswoman left open the possibility that there could be further changes in the coming days, saying the bill was “going through parliament; it is not yet on the statute book”.

Asked if there was truth in the suggestion that No 10 was worried about alienating trade unionists before the EU referendum vote, she said: “What is driving our approach is making a step change forward in balancing the interest of the unions against the majority of people who rely on the services they provide.”

Trade unions have bitterly resisted the reforms, branding them ideological and an assault on fundamental human rights.

Before the concessions were unveiled, Frances O’Grady, the general secretary of the TUC, said she had resented having to fight the battle against the trade union bill at a time when she could be working to convince left-leaning voters that Britain should remain in the EU.

“In a practical way, I have been going up and down the country banging on about the trade union bill, when I would much rather be spending at least some of my time going up and down the country banging on about why a Brexit would be a big gamble on workers’ rights and jobs,” she said.

”I think maybe the penny is starting to drop that in terms of grassroots organising capacity; in terms of having 200,000 workplace representatives who are often opinion leaders in the community, too, that it doesn’t make sense to be hammering us at a time when most people have no idea of why they’ve picked on us in the first place.”

The unions and Labour have not yet responded to whether the concessions go far enough, but Katie Ghose, chief executive of the Electoral Reform Society, said they were much-needed changes.

“The decision to give unions a year to transition towards making members opt in to their political funds is a positive step,” she said. “This 12-month period is a real window of opportunity for all parties to get around the table and sort out our broken party finance system once and for all.

“The public are sick and tired of party funding scandals, so the government and opposition should use this time to thrash out a genuine cross-party deal. A year is a long time in politics; it shouldn’t be beyond the parties to agree on a fair and transparent funding system in that time.”