There are reports that even if the government lost a vote of confidence the bold Boris would refuse to resign, and thereby creating an impasse that could be dragged out so as to allow Brexit to happen by default. I saw a comment somewhere that even if Westminster was paralysed it could be that, in view of the urgency, the Queen could intervene - it seems possible, albeit unlikely, but then the current situation is unique in the political history of the UK.
Some points taken from here -
https://en.wikipedia.org/wiki/Reserve_powerTo refuse to dissolve Parliament when requested by the Prime Minister. This was last reputedly considered in 1910, but George V later changed his mind. Harold Wilson, leading a minority government in 1974, was advised Elizabeth II might refuse to dissolve Parliament if she could identify an alternative Prime Minister able to command a cross-party majority.
To summon and prorogue parliament
For example, in the hung parliament in 1974, the serving Prime Minister Edward Heath attempted to remain in power but was unable to form a working majority. The Queen then asked Harold Wilson, leader of the Labour Party, which had the largest number of seats in the Commons but not an overall majority, to attempt to form a government. Subsequently, Wilson asked that if the government were defeated on the floor of the House of Commons, the Queen would grant a dissolution, which she agreed to.
Since it seems, from reports, that part of the 'no deal' plan is to ensure that there is no time for a GE before 31st October, because parliament is in recess, could be dealt with if the Queen could be persuaded (not sure by whom) to summon parliament to allow a vote of no confidence and then dissolve it if the government loses.
It seems unlikely the Queen would get directly involved, but these are unusual times. Get some popcorn in now, since if Brexit happens there might be none in the shops.