Tesco has removed the drinks from its stores in Marylebone, Victoria and Pimlico, as part of a Westminster City Council initiative to tackle street drinking.
Waitrose, Budgens, Londis and Threshers have also agreed to stop selling strong alcoholic drinks in Central London.
If successful, the initiative may be extended across Britain, which could put pressure on other stores to follow suit.
A spokesperson for Tesco said that it would be looking at the results "very closely".
Westminster City Council is also enforcing a borough-wide controlled-drinking zone and confiscating alcohol from street drinkers.
Carlsberg Special Brew is one of the strongest lagers freely available in the UK, with an alcohol volume of 9% and 4.5 units in one can. Diamond White cider has a volume of 7.5%.
Sir Simon Milton, leader of Westminster City Council, said: "We should be treating the sale of alcohol in the same way we treat tobacco -- with all the relevant pricing restraints and health warnings.
"The government needs to get a proper handle on this and come up with a robust national policy to deal with what is a rapidly growing problem."
Last week, Tesco said that it was willing to co-operate with the government on proposed legislation to ban the sale of cheap alcohol in the UK.
Under competition laws, supermarkets cannot collude to change alcohol prices, and would need government assistance if the national retail price of alcohol were to change.
The announcement followed intense criticism from some MPs in the last year that supermarket chains were fuelling a binge-drinking culture in the UK by selling alcohol at very low prices.