I should have added that BD also operated transatlantic charters in the 1970s, with turbo-jet powered 707s. When BD first acquired 707s from Pan Am (G-AYBJ was the first, I think), they were used on what was known as affinity group charters to the US and Canada. In an era where buy-over-the-counter charters and cheap tickets just did not exist, airlines could offer cheap charters only to groups known as affinity groups - groups of people with a shared interest, where the aircraft was chartered by the group for a special purpose. So, the man in the street could not buy a charter ticket, but if he happened to be a member of the "Wallace and Grommit appreciation society", and that society had a genuine reason to need to fly to the US, that was alright.
There were so many bogus affinity groups set up that after a while, the various authorities started cracking down and a number of airlines got stung with fines. This was the era when Laker was campaigning to set up Skytrain, and eventually the bottom fell out of the market. Some airlines moved to scheduled service (Caledonian and Laker come to mind), some failed (Donaldson) and British Midland pulled out of long haul and offered their 707s, very successfully, for lease to embrionic carriers such as Sudan Airways, Kenya Airways, etc.
The 707 operation you originally mentioned, that ended 18 years ago, was on the tail end of that instant airline leasing operation.