The date when exempt charities must start registering with the Charity Commission has been put back until 1 June because of concerns about the impact on friends' organisations.
A parliamentary motion to increase the regulatory burden on charities that are currently exempt from registering with the commission was due to come into force on 1 April.
But Labour peer Baroness Crawley announced at the end of a debate in the House of Lords on Tuesday that the date had been put back two months to give friends' organisations more time to prepare.
The Government is introducing a 'principal regulator approach' under which many exempt charities will have to report to existing regulators in their sectors, such as the Higher Education Funding Council for England, which will become responsible for ensuring compliance with charity law and will refer difficult cases to the Charity Commission.
Where no principal regulator exists, charities with incomes above £100,000 will be required to register with the commission.
Tory peer Viscount Eccles said there had been no formal public consultation or impact assessment about removing exempt status from groups such as friends' organisations, university colleges and halls, higher education institutions in Wales and the Museum of London.
"We lack that evidence," said Eccles. "Instead we have draft regulations, sketchily explained and unilaterally imposed by the Cabinet Office on behalf of the Office of the Third Sector."
He suggested consideration should be given to abolishing exempt status and making all charities register with the commission.
Eccles said he had heard that there were "already issues between the commission and an Oxford college or two" about the impending removal of exempt status.
"I doubt whether the commission has had any experience of dealing with charities such as the Oxford colleges, some of which have been going for rather a long time and have statutes and ways of doing things that are quite particular," he said.
Eccles, a member of the Friends of the British Library, said friends' organisations linked to institutions regulated by organisations other than the commission might be forced to de-register as charities, which would damage public confidence and lead to a loss of Gift Aid.
Crawley said it appeared that friends' organisations governed independently would remain registered with the commission.
But she said implementation of the motion was being delayed to allow more time for consideration of the issues relating to friends' organisations.