As I said above, London-Vienna is too long for a through sleeper these days. Sleepers can be commercially viable up to around 12 hrs, beyond which they only tend to exist when national governments are willing to pay extra to secure a through service (the Amsterdam sleepers fall into this category, the Dutch government paid OBB to extend them from Düsseldorf; the various sleepers from European cities to Moscow are another example).
The main benefit of sleepers compared with conventional or high speed trains is that you can sleep through the night on a through train, you don't have to get up at 3am to change trains. Before 20:00 and after 09:00 passengers will be up anyway so they may as well change trains for high speed ones.
London to Hamburg, Berlin, Munich and Zurich are in the right sort of range. Remember that sleeper trains often involve an element of portion working in order to serve more origin/destination pairs without the passenger needing to be woken so you need to account for an hour or two of shunting during the journey.
In fact, I welcome not having to change. I'd rather spend a few hours extra end-to-end than have to be booted out at breakfast time and then change trains, even if that second train does the remainder of the journey more quickly.
Having your own (continuous) space in which to work, snooze, chat, read, whatever - if you're in a sleeper berth - with breakfast while you're on the move, is convenient, and less faff.
In the days before the Baltic states joined the EU, and they still had a rail network connecting the 3 countries, I did a Tallinn-Warsaw journey on a very-much-not-high-speed through sleeper train which was a bit "clunky", with at one point a long stop to wait for another service to meet up with it and be tagged on (in Vilnius, awaiting the St Petersburg portion), and it was certainly a literally round-the-clock trip. But reasonably comfortable, relaxed, time to get on with my reading and writing, fascinating places to look at en route, interesting people to talk to (if I wanted to). There were chances to stretch my legs at a couple of places en route if I wanted to; all in all perfectly acceptable, and I doubt I'd have been bothered with arriving in Warsaw a bit sooner the next morning by changing for the last stretch, even if it had been an option.
(The only down side was the still-old-fashioned way of changing the bogies at a Belarusian border station [the through route traversed a little corner of Belarus]. Not that I minded a bit of clattering and jolting in the night in itself, but the Belarusian border guards took the opportunity of the train being stuck there for ages to go through the train trying to get money for technically unnecessary "transit visas". I got hauled off the train when I stood my ground, and ended up arguing with a bunch of them in a shed by the side of the track for most of the duration of the - slow - bogie changing procedure.)