Wakefield-based charity Penny Appeal is working with the Faiths Forum for London and the British Red Cross to distribute water, food parcels and blankets to those who have lost everything.
They have been given responsibility for distributing hot food to 300 people who have been made homeless at the Westway in London.
And they have appealed to people in the region to make a cash donation. They have been inundated with blankets and clothing and don't need any more - but still are accepting sanitary products and phone chargers.
A team was scrambled as soon as news of the tragedy broke and were among the first charities on the scene.
They are being joined today by another dozen members from Wakefield, Leeds and Bradford. More are en route from the Midlands and Manchester.
More than Â£1 million has been raised to help those affected as fire tore through the 24-storey building while volunteers and charities helped feed and shelter people who could not return to their homes overnight.
The charity's chief executive Aamer Naeem said they would be doing all they could to help in the coming days and weeks.
He said: "There's been so many people affected - people from Wakefield with relatives who lived in the block.
"One of the ladies found out that her nieces passed away, but her sister-in-law is still missing.
“We have a team on the ground, including our Head of Programmes and are coordinating with local partners including the Faiths Forum for London and The British Red Cross.
“We are also coordinating aid with the Sikh communities in Yorkshire and will be disseminating aid over the next few days as appropriate.
“Whilst our courageous emergency services are in their rescue phase, our team, and many others are working to make sure those affected know they are not alone.”
Call 03000 11 11 11 to donate or volunteer.
Penny Appeal shops in Bradford, Manchester and Birmingham are also accepting donations.