Dozens are thought to have arrived at the Kent port yesterday, among thousands to make the crossing in the past few days.
It comes as Home Office minister Damian Hinds said he expects a £54million payment promised to France for immigration controls to be transferred "in the coming weeks".
Mr Hinds said: "We are working closely with the French.
"I would like to see increased activity, increased turnback. France is a safe country. If you are seeking asylum you should claim it in the first safe country you come to."