Well, these days you can catch a Flixbus from London to Sofia for a mere 150 Europounds, and 48 hours of your time. And from there, Calcutta can't be that far, right?
(But, seriously, you can probably do it in another 48 hours...)
My Google Maps algo will be massively confused by my 'Directions' search: Sofia, Bulgaria to Kolkata, India on a Friday afternoon in January
You just need a nuclear-powered Big Bus.
https://image.tmdb.org/t/p/w1066_and_h600_bestv2/l5n4h4gmRtj...
https://en.wikipedia.org/wiki/The_Big_Bus
"Cyclops has a passenger capacity of 110 and is equipped with a bowling alley, Asian-style cocktail lounge with a piano bar, swimming pool, Bicentennial dining room, private marble-and-gold bathroom with sunken tub, and chef's kitchen."
From Sofia to the West of Turkey should be relatively easy. After that, travel through Iran, Afghanistan and Pakistan will get hairy.