The government has agreed to pause the lobbying bill in the Lords for as long as six weeks to give ministers time to rethink plans to regulate the way charities campaign, especially during general elections.

Ministers were forced into the concessions after they risked encountering a coalition in the Lords – led by crossbencher Lord Ramsbotham – which would have forced the bill into a select committee for consideration for up to three months.

Ramsbotham said he risked the opprobrium of some charities by not pushing for a vote on the bill, which has been widely criticised for gagging charities, but he said the government's integrity was now on the line.

An alliance of charities, thinktanks and NGOs are furious that the government introduced changes to the regulation of the political activities of charities without prior consultation.

The bill lowers the threshold that a charity is allowed to spend in the runup to the election without needing to register with the Electoral Commission from £10,000 to £5,000 in England.

Lord Wallace, handling the bill in the Lords for the coalition, has written to peers saying: "We are looking again at the thresholds for registration to ensure that small campaigning groups including charities are not caught by the regulatory regime." He promised to raise the threshold substantially, but government sources refused to confirm a figure.

Wallace has also agreed to review the limits being imposed on the amount third parties can spend in each constituency. The bill had proposed that a charity could only spend up to 0.05% of the total of the maximum campaign expenditure limits in any particular parliamentary constituency. For UK parliamentary elections, the maximum spending is £18.96m in Great Britain, so the cap equated to about £9,480 for each constituency.

The charities welcomed the pause, but Sir Stuart Etherington, chief executive of the National Council for Voluntary Organisations, called for real change including the abandonment of measures that would create "alarming levels" of red tape for charities, such as asking them to account for staff time.

"Similarly, asking charities working in coalitions to each account for the spending of the entire coalition remains unfair and unworkable."

Lady Hayter, the shadow cabinet office minister, warned the legislation would "wrap up charities in red tape" and threaten free speech and freedom of assembly.

She said: "What we need is much more of a commitment from the government not just to listen and engage – welcome as that is – but to act on what is heard. The third sector is not just looking for reassurance, it is looking for change".