The Sangatte camp closed its doors to new entrants on Tuesday, 10 days ahead of schedule.
"Any deal on Sangatte is a matter for the UK and the French, " said a spokesman.
What will happen to those immigrants who arrive at Sangatte after 15 November?
Calais' "jungle" has replaced official refugee centres like the now-closed Sangatte as a gathering point for migrants hoping to cross to Britain.
French president Nicolas Sarkozy was instrumental in closing Sangatte when he was interior minister and Mr Ashworth has written asking him to intervene again.
BBC: NEWS | UK | England | Kent | MEP backs Calais migrant centre
Mr Lubbers said in the Guardian the UNHCR's assessment is that only a limited percentage of the people in Sangatte would prove to be refugees.
Other measures have included closing the Sangatte refugee camp, tightening security at the Channel Tunnel and using scanning equipment that can find people hiding inside vehicles.
BBC: NEWS | UK | Politics | Immigration checks move to France
The town hall is reluctant to provide more permanent shelter in case, like Sangatte, it should act as a magnet and swell the migrant numbers further.
But since Sangatte's closure, migrants have had nowhere official to stay in the town and aid agencies say there is a strong humanitarian case for providing them with shelter.
The new centre has been dubbed "Sangatte 2" but the Calais mayor says it will be different because it lacks sleeping facilities and will provide only food, showers and information.
BBC: NEWS | UK | England | Kent | MEP backs Calais migrant centre
The bill is a key part of a deal struck by Home Secretary David Blunkett with France, which earlier on Tuesday announced the early closure of the controversial Sangatte refugee camp, near Calais.
"From today, the Sangatte centre will no longer draw would-be illegal immigrants to northern France and traffickers will no longer be able to use it to ply their evil trade in human life, " Mr Blunkett said.
Mr Blunkett said that the new system should send a message to the world that Britain is not open to abuse, and try to deter refugees at the notorious Sangatte camp near the French coast from risking the trip across.
Last week he was in London to announce that the Sangatte refugee centre, the camp near Calais from which in the past three years some 60, 000 would-be asylum-seekers have sought to enter Britain, would be closed on December 30th, four months ahead of a schedule agreed with the British.
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