It would still be weighted to London/SE demand. It's closest to Europe in journey times, in affinity (second homes, EU citizens, business travel) - and frankly, it has higher income levels.
If there were sleeper services to e.g. Bordeaux, Marseille, Barcelona - to name three, they would live and die on London demand. And they still be relatively seasonal! Paris/Amsterdam are too close. Geneva is interesting, with a mix of business, VFR, and year-round leisure - and mid-distance. Milan and Berlin seem in that sweet spot too, potentially. Barcelona has a similar mix, but is much further.
Also let's not be too self-centric - it goes two ways; inbound demand from Europeans to London specifically. Same for Scots - they aren't going to Sheffield or Leeds in droves, nothing there they don't have - they need London, hence the service.