The London theatre agents Samuel French represent the Asquith estate for all non-Peter Pan plays and might be able to help you with a contact. www.samuelfrench.co.uk
Otherwise, as Andrew suggested, you'll have to track down Herbert and Cynthia's descendants. The website www.thepeerage.com is helpful (although not very user-friendly) for finding out the names of the children of Michael and Simon Asquith but doesn't of course give any other detail. However, I do remember Ivon Asquith, one of Simon's sons, used to work at Oxford University Press but a quick search indicates he may now be at Edinburgh University Press.
If you do find out more, please could you post any details on this website, for future enquiries? Many thanks!