It seems there is a campaign by a Labour MP, Andrew Dinsmore:
"The owner of an artwork identified as stolen by the Nazis ought to have the right to decide whether they wish for the artwork to be returned," he said.
"Some people may be happy for work to stay in public collections, but they should have the option. At the moment, they are not given that choice.
"No one knows how many artworks this will relate to but we shouldn't think that just because the war was 60 years ago that this has all finished."
Under the current legislation, all national museums and galleries are prevented from disposing of any of their works. They can only offer compensation to the owners, although private museums are able to return artworks and artefacts.
I'm not sure if this is an essential change. I think the UK policy which avoids costly litigation is a useful model. In the US, where nazi-era restitutions suits are the most common, claimants often get title to the disputed works. However in nearly all cases they sell the works anyway to satisfy the enormous legal fees often required to bring these successful claims.
Then in a response, the Department of Culture Media and Sport said, "The Government are committed to introducing legislation as soon as possible to allow all national museums, that are currently prevented from doing so by the acts of parliament under which they are founded, to return works of art spoliated during the Nazi era." It seems this legislation will be a component of the prospective Heritage Protection Bill.
One thing to watch closely will be how the legislation may permit institutions to return the work to claimants, a potential move which may signal a shift in the obstacles the British Museum may have in electing to return antiquities to their nation of origin. The debate over that question will likely feature in the consideration, as the Parthenon Marbles always seem to be overshadowing UK heritage policy.