There never have been international overnight trains to the UK - the "Nightstar" services were canned after a combination of the growth of LCCs and the Spruce Goose style overspecification of the carriages.

Not only that, but night services are being cancelled all over Europe - the demand is dropping, again thanks to a combination of high-speed rail, LCCs and decent budget hotel chains.

The only way of travelling overnight from North/Central Europe is to end up in the Netherlands, and take the (rather nice) overnight ferry from Hoek van Holland to Harwich. However, this berths in Harwich at 06:30am, with the connecting boat train arriving at London Liverpool St at 08:54, so you wouldn't make the tour.

So really, your only option is to fly the night before. There are some very cheap fares to STN, with a number of low-cost hotel options in the area (or between there and London) - for example, it's not too hard to get the Premier Inn (very decent budget chain hotel) at Stansted around £50/night (it's in the long stay car park, oddly) or the Tune Hotel at Liverpool Street, near where the Stansted Express train arrives, with a bit of advance booking, for as little as £20!

To be honest, with a bit of luck and advance booking, you could get the flight/hotel combo for a lot less than a night train would cost.