(Adds cabinet meeting, Hammond)

LONDON, July 18 (Reuters) - Prime Minister Theresa May told her ministers on Tuesday to show the "strength and unity" Britain needs, and to keep discussions private, blaming hostile briefings to journalists on colleagues who are "not taking their responsibilities seriously".

Since losing the Conservatives' majority in parliament at an election she did not need to call, May has been increasingly unable to dictate to her ministers, who have begun to air their disagreements in public.

Much of the criticism, briefed by anonymous sources in the British media, has centred on finance minister Philip Hammond, who has been attacked on his stance on government spending and his approach to Britain's departure from the European Union.

"There is a need to show strength and unity as a country and that starts around the cabinet table," May told her top team of ministers, according to her spokesman.

"She said the government would make better decisions if colleagues were able to hold open discussions but it was vital that discussions in cabinet must remain private," he told reporters.

"The PM said the briefings and counter-briefings over the weekend had been a case of colleagues not taking their responsibilities seriously."

Hammond was quoted as saying he believed public sector workers were overpaid last week, a statement at odds with many in the cabinet who want to increase pay to try to win back voters and seized upon by the opposition Labour Party.

Described as "an enfeebled chancellor" in parliament by a Labour lawmaker, Hammond said: "I don't know which planet he lives on but I have to tell you I don't feel particularly enfeebled."

Earlier Sky News said May, whose authority was shattered by last month's ill-judged election, had taken the floor at a summer party for Conservative lawmakers to tell them there should be "no backbiting, no carping".

"The choice is me or Jeremy Corbyn – and nobody wants him," May told her lawmakers, according to the Daily Mail newspaper.

"Go away, have a proper summer break and come back ready for serious business." (Reporting by Elizabeth Piper and Guy Faulconbridge; Editing by Robin Pomeroy)