He told the Daily Telegraph that numerous factors behind the increase in crossings are "outside of our control".
The main United Kingdom opposition leader Jeremy Corbyn said there was a "duty to reach out the hand of humanity" to people facing danger and seeking safety.
A Home Office spokesman said: "The group consisted of nine men, two women and 10-year-old child".
Sajid Javid is returning to the United Kingdom later today after cutting a family holiday short to tackle the crisis of migrants attempting to cross the English Channel. "Ultimately the buck stops with the Home Secretary".
Six Iranian men have been found on a beach in southeastern England, according to British officials, as the number of migrants making crossings of the English Channel in small boats from France continues to rise.
The group were spotted on the beach at Kingsdown, Kent, by local residents along with an inflatable boat.
The head of the National Crime Agency-led Project Invigor organised immigration crime task force Chris Hogben warned more crossings were "likely" in the coming weeks.
In his call with Mr Castaner, Mr Javid assured the French Interior Minister of the UK's commitment to supporting his country's efforts to tackle the problem, including by supplying personnel and equipment.
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Speaking to Tom Watson on LBC, Labour MP and chair of the Home Affairs Select Committee Yvette Cooper said that Mr Javid will face questions from the committee on the incident.
The spike over the Christmas period is "deeply concerning", the UK Immigration Minister Caroline Nokes said.
The "blue-on-blue" onslaught was spearheaded by Dover MP Charlie Elphicke, who condemned the Home Secretary's "half-hearted Dad's Army type set-up".
She added: "The co-operation between us and the French has been very effective and is ongoing. Illegal crossings have now been on the increase for more than two months and more needs to be done as a matter of urgency".
He said it was vital the United Kingdom struck "a balance between protecting them (migrants) and protecting our borders".
Twenty three migrants were involved in three separate rescues on the Kent coast overnight and this morning.
Lucy Moreton also said it was "very hard to know" how much the French authorities were doing to prevent people-smuggling from the camps housing migrants around Calais.
Rejecting Mr Javid's suggestion that increasing patrols would encourage more people to attempt the crossing, Mr Elphicke said: "You don't deter burglars by leaving your front door open".