Germany and France are pushing for a Europe-wide agreement with the United Kingdom on migration and asylum, seeking to leverage the new UK Labour government's more "constructive" attitude toward EU-UK relations.

German Interior Minister Nancy Faeser and her former French counterpart Gerald Darmanin, who was recently replaced in a government reshuffle, addressed the European Union's home affairs commissioner in a letter, saying Brexit had severely affected migration policies.

"We believe that Brexit has had very detrimental consequences for the coherence of our migration policies. The absence of provisions governing the flow of people between the UK and the Schengen Area is clearly contributing to the dynamics of irregular flows — and to the danger posed to people using this route in the Channel and the North Sea," said the letter, first reported by Agence France-Presse.

"The arrival in office of a new British government, demonstrating its intention to cooperate constructively with the EU, seems to us to be conducive to concrete progress on this issue."

UK Home Secretary Yvette Cooper is due to meet with her counterparts Faeser, French Interior Minister Bruno Retailleau and Italian Interior Minister Matteo Piantedosi at a G7 ministerial meeting in Italy on Wednesday.

The Times newspaper reported that the UK government's willingness to cooperate with the EU on illegal migration, especially regarding English Channel seaway crossings, may be met with EU demands for legal asylum routes and a quota system for distributing asylum-seekers across Europe.

A source close to the UK home secretary cited by The Times indicated that while the government is open to cooperation, it would resist any EU proposals that could increase net migration or involve Britain in European migrant quotas.