Andrew Lloyd Webber was going to do a musical version starring Sarah Brightman for TV in 1989 -- oddly enough, Sarah Brightman does, or did, actually resemble Jessie, and she certainly has the vocal talent. Might have been interesting. Unfortunately Sonnie Hale's first wife, Evelyn Laye, threatened to sue if her name was so much mentioned in the production, which basically drove a coach and horses through the whole thing.

A well-reviewed stage musical based around Jessie Matthews' life and songs was produced in 2001 and played the West End in 2003: http://www.guidetomusicaltheatre.com/shows_o/over...
A soundtrack recording from this production was issued and is still available.

Vividly-written article, though I'd quibble with a few of the facts (i.e. the Lytton divorce was 1929, well before "The Good Companions") and the marriage summary is a little unfair on the men in her life -- no room to analyse here - I've managed to upload a commentary to http://blogs.myspace.com/index.cfm?fuseaction=blo...

She wasn't actually sacked from "Mrs Dale's Diary", although one gathers that was a possibility -- and after all, her predecessor had already been replaced in the part. (Odd, really, that Jessie Matthews is so associated with the programme, given that she only took over the role of Mrs Dale for a few years at the end of such a long-running series...)

Apologies if this comes out as terse: the browser has crashed on me ten or eleven times while trying to post, and it's driving me up the wall -- aarrggh!