Former Top Gear host Jeremy Clarkson and his daughter, Em, were among the first to tweet, appealing for people in Kensington to give what they could.
Virgin boss Richard Branson said the airline's not-for-profit foundation, Virgin Unite, would support people involved.
"I'm with my grandkids as I write, and it makes one want to weep when something like this fire happens. We've been involved in several fires over the years, but nothing like this, and know how lucky we have been to escape with only material things lost," he said.
Singer Rita Ora shared information on where victims could go for help as she shared her shock at the horrific fire.
Kiwi model Rachel Hunter also shared her love on Twitter.
