That's less clear: it depends on how she goes about it. Consider this: a) She convinces the Leader of the Commons to bring a motion to dismiss parliament (unde

That's less clear: it depends on how she goes about it. Consider this: a) She convinces the Leader of the Commons to bring a motion to dismiss parliament (under the 2011 Fixed Term Parliaments Act this requires a 2/3rds majority). b) She convinces the members of the Privy Council to form a National Coalition, and to stand as such for election on a manifesto centred on EU membership. Alternatively, she finds someone who can command the confidence of the House of Commons across party lines, and gets agreement across party lines (likely through the Privy Council) to support the appointment, and duly appoints them Prime Minister (this is roughly how Churchill became Prime Minister in 1940, with no election held since 1935 and none would be held till 1945). The cross-party Government then formed can then seek a mandate to remain in the EU in a number of ways (such as then falling to an election or a second referendum). One shouldn't understate the amount of influence the Queen can have, and maintain, if she plays her cards right.