Gone for a Burton is an expression in British English.
This expression developed from Going for a Burton, which has its origins in early training for air-sea rescue during World War II. RAF Coastal Command ran a programme of training for aircrew in Blackpool, England in 1944/1945. This involved learning how to inflate the life-saving inflatable boat in an emergency, and practising this by jumping, in full flying kit, off the top diving board at the Empire Baths, then one of England's larger swimming baths. Coastal Command ran this programme from an office which was above the Blackpool shop of the Burton Tailoring Group, then known as Montague Burton. Participants in the training had to register at the office above Montague Burton. Going for a Burton therefore meant having to jump down into the water, and came quickly to be used to describe any large fall.
Gone for a Burton developed from this to cover situations where a plane ditched in the sea and the change to the past tense came to imply fatality.
References
The original article can be found at Gone for a Burton and the edit history here.