I think the downs will see some settled snow. Tonight is tricky - there's reports of snow in Hampshire, probably as part of the snow shown here
My concern is that the rain is fragmenting and it will have decreased in intensity before any cold air gets a chance to undercut.
Thursday looks a...
My guess would be rain then snow mid Sussex, but snow most of the time in London, and it will freeze as soon as it clears, but they will be well after the football. I'd say it will be snowing for at least some of the game, which will be pretty on the telly.