BOA Charter did not have their own aircraft, but just used time on the regular BOAC fleet, which is doubtless why the same initials were employed.
BOAC had a couple of 707s rigged up in an all-Y configuration which were used on scheduled flights to Toronto and a few other places with a low first class demand, and these were what the charter side used. So it was really just a marketing front, the ops side was mainstream BOAC. The airline had always done oddball charters of course but this was a move into a more formalised structure.
This was all at a time when the major scheduled carriers were being hit by an increase in transatlantic charter competition, and wanted to gain some of this for themselves. The irony is the competition grew up mainly around the disposal by Pan Am of their early 707 fleet when the 747s came along; it was one of the earliest secondhand sales of good long-haul jet equipment. Likewise BOAC had 707s spare. Destinations such as New York, Toronto and Los Angeles were mainstream work, and to a lesser extent to the Far East.
Transatlantic charter flights to the USA reached their zenith in the early 1970s when ABC (Advanced Booking Charter) flights were allowed to be marketed to individuals, then lost ground after a few years to the scheduled carriers segmenting the market and offering comparable advanced purchase fares on their own flights as they moved over to widebodies and had the capacity available. Charters to Canada were in a different regulatory environment and continued, as to some extent they still do, but those to the USA died out long ago.