The Foreign Office is opposed to the participation of the Burmese military government until it releases the pro-democracy opposition leader, Aung San Suu Kyi.
But the French government is arguing that it is more important that the summit goes ahead.
A British government source described the French position as "craven". Britain has the support mainly of the former communist states of eastern Europe.
The Europe-Asian summit (Asem) is to be held in Vietnam on October 8 and 9. Tony Blair is unable to attend and is to be replaced by the deputy prime minister, John Prescott.
Asean, the Asian partner in the venture with the EU, has invited Burma, Cambodia and Laos to join the forum for the first time to balance the arrival of 10 new EU countries.
A French foreign ministry spokesman said: "The Asem meeting is so important to our Asia policy that it needs to go ahead. Burma is a relatively minor issue, next to all the other things Europe needs to engage with Asia on. A row over Burma should not stop the meeting from going ahead."
A Foreign Office spokesman said yesterday: "We are working closely with our European partners on the issue. The European foreign ministers are agreed on the importance of the Asem summit but also that Burma is a problem."
European foreign ministers are to meet next week to try to resolve the dispute. A special EU envoy, the former Dutch foreign minister Hans van den Broek, has been trying to find a solution.
The likely compromise is that Burma will be invited but at a lower level of representation than head of state to register disquiet over the country's human rights record, including the arrest of Ms Suu Kyi. The Foreign Office is likely to accept such a compromise in public while remaining privately unhappy that the EU failed to stand by the demand that Burma not be allowed to participate until she was released.
