Mrs Lawrence said the money raised by the concert would help her foundation, which has struggled for funding in recent years, to continue its work for another 20 years.
Speaking after the launch event at Abbey Road studios, she said that she would like to see the Government provide more funding.
She said they had received some emergency funding from the Home Office, but added "we shouldn't have to do that".
"We shouldn't have to think 'that's just a one-off'. They should look to continue to do it," she said.
"They have seen the work that we do, they have seen the progress we have made, they have seen all the opportunities that young people have had since they have been at the Stephen Lawrence Centre.
"I think that should be something that makes them say: 'Ok, we want to support an organisation like you, you can make a difference to so many young lives, get them off the streets, get them into education, get them into a profession.'
"That is what I would like to see the Government do a lot more of."
More top news
The unlicensed events unfolded on Saturday night at Clapham Common and Tooting Bec Common.
A 37 year old man who was taken to hospital after getting into difficulty in a stretch of water near Maidenhead has died.
Jonty Bravery, who is mentally ill, has been jailed for 15 years after throwing a six year old boy from the Tate modern balcony.