The football associations of England, Northern Ireland, Scotland and Wales announced last month they would submit a joint expression of interest in hosting the finals in 10 years' time.
The deadline for initial expressions of interest passed on Monday and although Spain's federation president Rafael Louzan last week announced his country's intention to bid alongside Portugal and Morocco, Infantino indicated the UK bid was the only one being considered.
"We received one bid for 2031 and one bid - one valid bid I should add - for 2035," he said at the UEFA Congress in Belgrade.
"The 2035 bid is from Europe, from the home nations."
The UK bid will now go unopposed to FIFA Congress in the second quarter of next year where it could be voted through by acclamation, as the Saudi Arabian bid for the 2034 men's World Cup was last December.
The UK bid will still be subject to the usual FIFA checks, such as an evaluation report.
Infantino confirmed the United States were the sole bidders for 2031, potentially alongside other nations from the CONCACAF confederation which covers North and Central America and the Caribbean.
"The path is there for the Women's World Cup to be taking place in 2031 and 2035 with some great countries to boost even more the women's football movement," Infantino added.
The 2027 edition with 32 teams is being hosted by Brazil.
The Women's World Cup would return to the US for the first time since the 2003 edition. The US also hosted in 1999.
In a further boost for women's soccer, Infantino detailed FIFA's plan to have more women's teams than men's playing at the next Olympics.
There were just 12 teams in the women's tournament at the 2024 Paris Olympics and 16 in the men's tournament.
Though the International Olympic Committee strongly supports gender equality at the games, adding four more women's teams — and about 70 extra players, plus team officials — would push the limit of agreed athlete quotas for organisers in Los Angeles.
Infantino said on Thursday that FIFA's new proposal is to flip the numbers to have 16 women's teams and 12 in the men's tournaments.
The final decision is for the IOC, which has an executive board meeting next Wednesday.
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