Officials at the Department of the Environment want to pour paraffin over the birds' eggs as a 'socially acceptable', but at present illegal, type of birth control. And the Heritage Department has already shot 100 of them secretly at dawn on Bird Island in St James' Park, the very place where they were first introduced to Britain from North America, as an ornamental species, by Charles II 325 years ago.
The numbers of Canada Geese, the football hooligans of the bird world, is doubling every eight years. Forty years ago there were only 2,000 in Britain, now there are well over 60,000, and by the end of the decade there will be around 120,000.
They are aggressive, crowding out other waterfowl, and attack children trying to feed the ducks. They damage crops and strip the banks of ponds and lakes of grass.
Cursed with regrettable digestive systems, they produce prodigious amounts of slimy green excrement - each bird deposits an inch-and-a-half long dropping every three or four minutes.
They have no natural predators here (even foxes are reluctant to take them on). They can live for 12 years, and they are protected under the Wildlife and Countryside Act.
They also have famous friends. Two years ago London's Wandsworth Council was forced to abandon plans to kill 200 of them in Battersea Park after a campaign led by writer Carla Lane, who created the TV series Bread, and by Linda McCartney. The fight got so fierce that Rentokil, the company hired to carry out the cull, refused to do the deed, fearing 'irreparable' damage to its reputation.
The RSPCA decries 'character assassination of a species' while the RSPB says 'Canada Geese should be innocent until proven guilty'. Chastened by this fiasco, Whitehall has set up a working group, including conservationists, hunters, bureaucrats and Wandsworth Council, to come up with a 'humane solution'.
The group has just come up with the idea of coating the eggs with paraffin, but this is banned by the Ministry of Agriculture.
Park keepers in Milton Keynes take the eggs from nests, soon after they are laid, cook them in a tea urn and return them, thus fooling the parents into going to work on hard-boiled eggs. Bromley Council puts trip wires around its ponds to stop the geese waddling on to the grass.
Privately many members of the working groups say that killing geese is the only effective solution. Hunters can already shoot them in the spring and summer, but are forbidden to sell their carcasses, and have had little impact on the population. And so far, the Government has been wary of ordering an organised slaughter.
The Heritage Department last week admitted to the Independent on Sunday that they had secretly shot 100 geese in St James's Park in the early hours of one morning last July. Asked why it had not made it public, a spokesman said that was part of 'the normal day-to- day management of wildfowl', before confirming that it was 'unprecedented'.
One senior Environment Department official has his own solution: he ate a Canada Goose for dinner last New Year's Day. 'People say they are inedible,' he said. 'They may taste a bit gamey, but they make jolly good eating.'