Section 2 of the Act also provides for two ways in which a general election can be held before the end of this five-year period:[2]
If the House of Commons resolves "That this House has no confidence in Her Majesty's Government", an early general election is held, unless the House of Commons subsequently resolves "That this House has confidence in Her Majesty's Government". This second resolution must be made within fourteen days of the first.
If the House of Commons, with the support of two-thirds of its total membership (including vacant seats), resolves "That there shall be an early parliamentary general election".
The Conservatives could certainly manufacture a situation where a simple majority would force an election, but it would mean replacing most of the current government. I did wonder a few days ago if that was what some back benchers are up to with their treatment of Hammond, etc, but I was shouted down on here.
I don't think two-thirds would call for an election without a vote of no confidence.