without any real knowledge of the GB programme, id say operating in triangle pattern would be near on impossible within a standard FDP.
Remember every sector reduces ( on average ) 45 minutes from the allowable FDP, coupled with the extra down time id say you'd struggle to operate this in 12:30 minutes ( which is the most allowable if the flight departs LGW between 0800 - 1259 ).
Like i say, just looking at the crewing side, but its gonna be close!!
Discretion, discretion...!!!??