The IOC is facing a mounting backlash after setting out a pathway in January for competitors from Russia and its ally Belarus to earn Olympic slots through Asian qualifying and to compete as neutral athletes in Paris.
Britain's Culture Secretary Lucy Frazer addressed the letter to the UK chief executives of 13 of the Olympics' biggest sponsors, including Coca-Cola, Samsung and Visa, outlining the government's concerns.
"We know sport and politics in Russia and Belarus are heavily intertwined, and we are determined that the regimes in Russia and Belarus must not be allowed to use sport for their propaganda purposes," Frazer wrote.
"As long as our concerns and the substantial lack of clarity and concrete detail on a workable 'neutrality' model are not addressed, we do not agree that Russian and Belarusian athletes should be allowed back into competition."
Ukraine has threatened to boycott the Paris Games if Russian and Belarusian athletes compete.
The British government issued a joint statement last month with 34 other nations calling on the IOC to ban Russian and Belarusian athletes from its competitions.
The IOC issued sanctions against Russians and Belarusians after last year's invasion of Ukraine but is reluctant to exclude their athletes from the Olympics entirely for fear of a return to the days of the boycotts of the Cold War era.
Neutral athletes at the Olympics are not considered to be representing their nations and their successes are not accompanied by the flying of flags or playing of national anthems.
Most international sports federations have excluded athletes from the two countries since the invasion but some are now starting to allow them back into competition.
"Noting the IOC's stated position that no final decisions have been made, we have strongly urged the IOC to address the questions identified by all countries and reconsider its proposal accordingly," Frazer wrote.
"As an Olympic partner, I would welcome your views on this matter and ask you to join us in pressing the IOC to address the concerns raised in our statement."
