Premier League clubs should not be allowed to have betting firms on their shirts, a House of Lords Select Committee report has recommended.
The cross-party committee, set up to look at the impact of the UK's gambling industry, also says such sponsors on Championship club shirts should be phased out by 2023, and that other sports should end shirt betting sponsorship in three years.
This season, half of Premier League clubs and 17 of 24 Championship clubs are sponsored by bookmakers.
The recommendations are part of a 192-page report warning more needs to be done to prevent gambling-related harm, with the Gambling Act 2005 under review by ministers.
Campaigners believe betting has been normalised within football and can lead to addiction.
The committee's recommendations also state: "There should be no gambling advertising in or near any sports grounds or sports venues, including sports programmes."
But the report says restrictions on shirt sponsorship and other advertising "should not take effect for clubs below the Premier League before 2023. A similar flexibility should be allowed in the case of other sports".
It added: "These restrictions should not apply to horseracing or greyhound racing."
The report said removing betting sponsorship entirely would "not unduly harm Premier League clubs but it would very probably have a serious effect on smaller clubs.
"We therefore think they should be given time, perhaps three years, to adapt to the new situation. They would not be allowed in that time to enter into new sponsorship contracts with gambling companies, but any existing contracts could continue until they terminate, and clubs would have time to seek alternative sources of sponsorship."
The English Football League (EFL) says the gambling sector contributes £40m a season to the league and its clubs and with the financial problems of the coronavirus pandemic, this "significant" contribution is "as important now as it has ever been".
It also says working to prevent gambling problems with the betting companies is of "greater benefit" than a ban.
In a response to the Lords' report, the EFL said in a statement: "The association between football and the gambling sector is long-standing and the League firmly believes a collaborative, evidence-based approach to preventing gambling harms that is also sympathetic to the economic needs of sport will be of much greater benefit than the blunt instrument of blanket bans."
The Premier League, which unlike the EFL does not have a betting partner, has said it would be a "welcome participant" in the government review of the Gambling Act.
Chief executive Richard Masters has previously said gambling needs stronger governance, but says it is up to individual clubs whether they want relationships with betting firms.
He also told the BBC he did not think clubs having gambling sponsors directly linked to people becoming more vulnerable from betting.
The Lords report also mentioned how a 'whistle-to-whistle' ban on gambling advertising from five minutes before to five minutes after a match "is of very limited use when viewers, including children, can throughout the match see a plethora of gambling advertising on shirts and on the perimeter - and when they are in any case likely to be watching outside that whistle-to-whistle time".
Chair of the committee, Lord Grade said: "Most people who gamble, enjoy it safely.
"However, gambling related-harm has made the lives of two million people miserable. It leads to hundreds of people each year taking their own lives, leaving families and friends devastated."
James Grimes, a former gambler who runs charity The Big Step which is tackling football's relationship with gambling, said: "We welcome the recommendation to remove gambling sponsorship and advertising in the Premier League immediately.
"We've been calling on government and football to reduce gambling exposure to children, in order to prevent young people going through the same thing that I did.
"Gambling advertising in football is at saturation point and it's normalised harmful products and practices to young people. No child should be exposed to adult products as prevalently as it is with gambling in football.
"Premier League football has a responsibility to prevent gambling exposure to its young fans, which make up a quarter of its audience."