The world I'm in, the year is 1977, but this, and other rounds in the general time era, I've usually had great luck with the Tu-114D, it has a range of about 6500 nautical miles, speed of 432 knots (ok, not the fastest, but still not the slowest either), and 120 seats, and costs about some 75 mil to buy new. The aircraft is fairly flexible (and by that, I mean simple to use in a variety of situations) in my opinion, so even those who operate out of airports with 2 million pax could possibly pull a nice profit and keep it for a few years. Downside for you, in 1981, it's discontinued that year, so order up as much if you can if you find them interesting. In the years it's offered, it's possibly the most ordered long range aircraft simply because of those reasons! Sort of like how (and I'm tangent from airlines here into railroads), how the PKP Class EU06 and 07 has operated for almost 50 years.
If you want a very rough estimate if it could do those routes 2x, you can go to the Great Circle Mapper (link:
http://www.gcmap.com/ ), set up the route you want, here is JFK-LHR with a 2x freq. applied and the L1011-500's speed:
http://www.gcmap.com/mapui?P=LHR-JFK-LHR-JFK-LHR-JFK-LHR-JFK&MS=wls&DU=nm&SG=525&SU=kts39 hours, so definitely out of the question. A lot changes between 77' and 81' though, so I can't say if there will be faster, non- supersonic planes that can do it off the top of my head in the game by then. If you could get something with a 600 kts or 700kts, you may be lucky there.
As for 747s and fuel efficiency? I suppose if you can make good profit off them, then they're good! The problem with 747s is their price. They are quite expensive aircraft to buy, and since the Maintenance is still a function of the MSRP and the age of the aircraft, it makes it a VERY expensive plane to own, but seeing you're out of LHR, you can possibly do something with it (though I would recommend smaller, cheaper aircraft if possible. The 747 in this game can do what the 747 did in the beginning, kill off a lot of airlines that wanted it because they just wanted a giant beer can in their fleet, but with no idea of how to use it properly.