The influx has led to increased tensions in the sparse woods where the migrants sleep and sparked fears that a new shanty town like the notorious Jungle could spring up.
About 100 migrants clashed with police at a food distribution point close to the ferry port on Thursday night when the migrants threw stones at the officers who responded with tear gas.
Charities said there had been 200 new arrivals since Mrs May announced the accelerated procedure after talks with French President Emmanuel Macron earlier this month.
There are now thought to be between 800 and 900 migrants from Eritrea, Ethiopia, Afghanistan and elsewhere in Calais.
The French interior ministry said about 100, mainly children, had arrived in the town since Mrs May’s pledge.
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Downing Street denied the Sandhurst Treaty, drawn up after intense lobbying by Mr Macron for Britain to take more migrants, would encourage more people to try to reach the UK.
The treaty says adult asylum-seekers wanting to cross the Channel to join family in the UK will have their claims processed in a month, compared with up to six months at present. The period for children will be 25 days.
Mrs May also promised an extra £44 million to reinforce border security.
A spokesman for the Pas-de-Calais prefecture said the extra migrants had come to Calais from other French cities, where many sleep in shelters or on pavements.
A spokesman for the charity L’Auberge des Migrants said 200 men, women and children had arrived in Calais in the hope of being fast-tracked to Britain.
He said: “They thought they would be put on to a coach and allowed to cross the Channel.
“We’ve had trouble giving food to everyone because of the influx.”