British United were a Viscount operator (which Braniff were not) and were closely involved with the One-Eleven design finalising, which BEA were not interested in. BUA placed the first order for it, in May 1961. Braniff followed in October 1961.

British United was formed from the merger of three independent UK airlines, Airwork, Hunting-Clan, and Air Charter. Freddie Laker (not Sir Freddie until much later in life) owned this last one and became Managing Director of the new merged operation, buying both the One-Eleven and the VC-10. After an executive fight in 1966 he quit and started his own airline again, beginning by ordering his second fleet of One-Elevens, which took British (and West Berlin) holidaymakers down to the Mediterranean for many years and were still all in the fleet when Laker Airways finally went under in 1982 - all the Skytrain transatlantic operation came much later in the airline's life.

Quick question - what other British jet design did Freddie at Laker Airways place an order for ?