The track, which he recorded for the 2010 World Cup when it failed to chart, jumped 27 places overnight according to data from the Official Charts Company and is now just outside the top 10 at number 11.
Official Charts Company chief executive Martin Talbot said: "Rik Mayall's death this week was a shock to a whole generation of comedy fans - and their reaction in pushing his 2010 single is a reflection of how much he was loved.
"In turn, his new hit also underlines how the Official Singles Chart remains a modern-day barometer of public opinion."
The star, who died aged 56 at his London home on Monday, shot to fame playing poetry-writing anarchist Rick in The Young Ones.
Other roles included Lord Flashheart in Blackadder and the conniving Conservative MP Alan B'Stard in The New Statesman.
A post-mortem examination is expected to be carried out today to establish how he died.
An inquest may then be scheduled, depending on the post-mortem result.
Tributes have flooded in for Mayall since his death.
His daughter Bonnie said on Facebook: "My dad was loved not only by my family, but by many many others.
"We will never forget him and neither will the world.
"RIP to the man, the myth, the legend - my wonderful, generous, foul mouthed and hysterical father. My idol now and forever.
"We love you daddy."
His Comic Strip Presents... colleague Peter Richardson, whose son was one of the last people to see the actor alive, said he was happy and healthy in the hours before his death.
Richardson, who directed Mayall in a series of TV shows, told BBC Radio 4's Today programme that his son saw him around half an hour before he died.
He said: "He was happily chatting away and it was very quick, and we still don't quite know what happened, but it was a seizure of some sort."
Mayall, who leaves wife Barbara and three children, Rosie, Sidney and Bonnie, survived an almost-fatal quad bike accident in 1998 which left him in a coma for several days.
Richardson said: "He had 16 years after the quad bike and at the time I don't think people thought he would survive that but he lived for another 16 years and it was just shocking that he went - he was so happy and seemed very healthy when he did go."
Close friend and long-time collaborator Adrian Edmondson said he felt privileged to have shared good times with him at Manchester University, where the pair studied.
He said: "There were times when Rik and I were writing together when we almost died laughing. They were some of the most carefree stupid days I ever had, and I feel privileged to have shared them with him. And now he's died for real. Without me. Selfish bastard."
Stephen Fry, who also starred in Blackadder, said on Twitter: "Simply distraught to hear of the death of Rik Mayall. An authentic comedy genius and a prince among men."
Ben Elton, who was also a university friend of Mayall, said: "I owe him so much. He changed my life utterly when he asked me to co-write The Young Ones with him and he was with me on the day I met my wife. He always made me cry with laughter, now he's just made me cry."
Another less orthodox tribute - in the form of a makeshift blue plaque - was put up in Hammersmith, west London, reading: "Rik Mayall 1958-2014 Punched his friend in the balls on a bench near this spot."
A Scotland Yard spokesman said officers were called by London Ambulance Service to a house in Barnes, south west London, where "a man, aged in his 50s, was pronounced dead at the scene".
He added that the death was not believed to be suspicious.
Mayall was born in Harlow, Essex, to drama teacher parents and launched his comedy career on stage in a duo, the Dangerous Brothers, with Edmondson.