UKIP leader Nigel Farage has told Daybreak that "it would be difficult to see UKIP do a deal with the Conservatives all the while that man [David Cameron] is their leader."
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The move comes amid a motion of no confidence that was tabled against Labour leader Jeremy Corbyn.
The first anniversary of the Sousse terrorist attack - which left 30 Britons dead - will be marked by families of the victims on Sunday.
Since Friday's EU result, the Liberal Democrats have recorded thousands of voters signing up to become members.