Mike Adamson, chief executive of the British Red Cross, has called for a review of the voluntary sector response to UK-based emergencies after the Grenfell Tower fire.

Adamson said that although there was a lot to celebrate about the sector’s response, coordination could be improved and it was important to reflect on what could be learned from such events.

But he rejected calls for a domestic equivalent of the Disasters Emergency Committee. He said that the DEC’s focus was on raising money, something that had not been a problem in the wake of Grenfell or recent terrorist attacks because of the public outpouring of support.

“We need to be looking at how we frame the way in which the voluntary sector responds in a whole variety of ways in these kind of emergencies,” Adamson said. “We need to work out what is inevitable in an emergency situation and what we need to learn from and get right.”

For example, he said, the immediate aftermath of an event such as the Grenfell fire or a terrorist attack was always likely to be chaotic.

But he said responding to the fire had been much more complex even than the recent terrorist attacks, because of the need to support community recovery as well as the immediately affected victims.

A review, Adamson said, should look at “creating the mechanisms that allow coordination, fundraising and funding distribution for the medium term”.

He said: “We want to be engaging with government about what kind of arrangements we have in place for the future, for a terrorist attack or other emergency. How much do you have as a standing fund? How much do you set aside for immediately affected victims and how much do use for community recovery and development?”

Since the Grenfell fire, a number of people have called for a domestic equivalent of the DEC, a coalition of 13 charities that coordinates its members’ responses and fundraising efforts for overseas disasters.

Last month, the Charity Commission said it was in talks with a number of charities about a more coordinated response to disasters.

Adamson said the commission had been playing a helpful low-key coordination role with charities and community groups that were responding to Grenfell, but he did not believe a domestic DEC was the answer.

“The DEC raises money in partnership with the broadcasters for huge emergencies overseas affecting hundreds of thousands of people,” he said.

“There’s no shortage of money in the response here, but there are lots of different funds and what I think we need here is some improvements to the coordination of fundraising and funding distribution.”

But he said that any review and a wider debate about society’s response to Grenfell should happen in parallel with the continuing relief effort on the ground.

A commission spokeswoman said the regulator agreed there were lessons to be learned from the sector’s response to the fire and it would be working with charities to coordinate their responses in the future.

“In the short term, however, our priority is to help ensure those affected by the fire at Grenfell Tower know how to access the charitable support that is available to them,” she said. “We have supported and welcomed the collaborative approach that the key funders have taken in a complex environment.

“As the largest and most experienced charity on the ground in west London, the British Red Cross has a key role to play in making sure that happens.”