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Britain's Prime Minister Boris Johnson will meet his counterparts in Stockholm and Helsinki during a one-day trip on Wednesday, taking questions from media in both countries.
"We support countries' democratic capability to decide on things like NATO membership," Johnson's spokesman said.
"We understand the positions of Sweden and Finland and that is why the prime minister is going to discuss these broader security issues."
A formal application to join the North Atlantic Treaty Organisation could be made at the alliance's June summit in Madrid and is likely to be fast-tracked, though getting the signatures of all 30 alliance members could take up to a year.
Finland and Sweden would like to have some guarantees that NATO member nations would defend them during any transition period, when they would be applicants to the alliance, but not yet in.
Britain has been one of the strongest supporters of Ukraine's efforts to resist Russian forces since Russian President Vladimir Putin launched the invasion on February 24.
The government has sent anti-tank missiles, air defence systems and other weapons to Ukraine.
The Nordic region's defence capabilities would be strengthened if both joined NATO, allowing joint defence planning within the framework of the alliance, Sweden's defence minister told local radio on Tuesday.
"(If Sweden and Finland join NATO) there will be the effect that we use each others' strengths and advantages and fully complement each other and also carry out operational planning," Peter Hultqvist of the ruling Social Democrats said.
"If so, the effect will be that we become stronger together. This is something that can happen if we choose to join NATO."
Sweden already has defence agreements with its Nordic neighbours.
The Social Democrats will decide on May 15 whether to drop decades of opposition by the party to NATO membership - a move that would almost certainly lead to Sweden asking to join the alliance.
Finland, which shares a 1300km border and a difficult past with neighbouring Russia, is reconsidering its long-standing position to refrain from joining NATO in order to maintain friendly relations with its eastern neighbour.
Finnish president Sauli Niinisto is this week expected to announce his support for an application.
Denmark, Norway and Iceland are already members of NATO.