The 24-storey residential building in west London went up in flames just before 1am on Wednesday (14 June), with 12 people confirmed dead and more than 70 being treated at hospitals across the city.
The tower, which contained 120 flats, was home to 400-550 people, many of whom have now been left temporarily homeless due to the fire.
Singer Lily lives close to the tower, and reached out to offer her help to those in need of somewhere to stay.
Writing on Twitter, she said: “I’ve never seen anything like it in my life, praying people got out okay, woke[n] up by [the] sirens.
“A lot of people without homes here tonight. Not a lot of info. If anyone needs a bed or a lift or tea, tweet me and I’ll follow back.”
The star also urged her followers to donate items - including clothes, toiletries, sanitary products, portable phone chargers and toys - to the appeal at Clements Church in Kensington.
Jamie Oliver has also offered free food to those affected at his nearby restaurant.
The celebrity chef owns Jamie’s Italian at the Westfield shopping centre in White City, which is just a 20-minute walk from Grenfell Tower.
Posting on Instagram, he wrote: “You are all welcome to come hang out in my restaurant and be fed and watered by my Jamie’s Italian team. We are in the Westfield just around the corner.
“Food and drink free of charge so just go and speak to my manager Juan and we will sort you out and give you some love.”
A number of online fundraising campaigns for the victims have already resulted in thousands of pounds worth of donations.
HuffPost UK has also been told that Westfield will pay for hotels for those in need.