Kevin Duncan very kindly put this summary together. I am of the opinion that these birds are of Continental origin and arrived during the cold spell with up to 1,600 other Barnacle Geese forced out by the freeze. Many of these Dutch birds of course are naturalised.
The following is list of the sightings of the 16 now 15 Barnacle Geese.
06/12: 16 first seen at Island Barn Reservoir, Surrey
14/12: Dorney Lake, Bucks
17/12: Dorney Lake, Bucks
Not seen when the snow was on the ground
30/12 Dorney Lake/Dorney Wetlands now reduced to 15 birds
01/01 Dorney Wetlands
02/01 Jubilee River, Marsh Lane, Bucks
08/01 Dorney Lake, Bucks
09/01 Dorney Lake, Bucks
10/01 Dorney Lake, Bucks