I've read it, and it involves 3 transferral. A direct train, which is amended to suit Austria and Hungary's signal systems, could condense the travelling time to around 12 hours. The train could depart at 8 am (London St Pancras) and arrive at 8 pm (Budapest Keleti)
The stops could be London St Pancras - (non-stop) - Köln Hbf - (non-stop) - Frankfurt (Main) Hbf - (non-stop) - Wien Hbf - (non-stop) - Budapest Keleti.
Trainsets: Class 373/374 (modified to suit Austrian and Hungarian Railway system)
Departure: each Monday, Wednesday, Friday and Sunday, 08:00 from London St P and 08:30 from Budapest Keleti, between December to January and July to August