British democracy is in limbo and it may not recover for years. There are parallels between the potential constitutional crisis and the 1953 crisis in Iran because neither Bojo nor Corbyn, both demagogues like Mossadegholsaltaneh, are trustworthy [Corbyn is a Closet Brexiteer, of that there is no doubt]. Both similar to Mossadegh are in conflict with their own parties and in the case of the incumbent prime minister Bojo in conflict with a dysfunctional parliament, similar to the 17th Majles, albeit for different reasons.

Mossadegholsaltaneh was advised by two of his legal advisers the constitutional crisis he delibrately created would give the shah legitemate basis for dismissing him but he stubborn Qajar rabble would not listen.

Bojo's hands are tied by the mess Cameron created. In additons to the ill-considered referendum for Brexit Cameron's govrerment introduced the Fixed Term Parliament Act. Bojo has no majority yet he cannot call for an election before 2022 if Corbyn chooses not to oblige as early elections require 2/3 majority vote. 

The constitutional issues are explained: here.

But the most interesting question is whether Bojo can ignore the parliament or refuse to coperate:

What if Boris Johnson simply refused to cooperate?

As already indicated, Johnson would need to remain as Prime Minister unless and until it was clear that an alternative government could be formed which could command confidence in his place.  He would thus remain the Queen’s principal constitutional adviser. However, since he no longer commanded confidence, his advice would no longer be binding. In essence, in these circumstances, it is parliament’s advice that the Queen is bound to take. If MPs had clearly indicated support for an alternative Prime Minister, Johnson would be expected to resign and to recommend that the Queen appoint the alternative candidate in his place (Cabinet Manual para 2.19).  If he refused to do so, the Queen would be entitled to dismiss him and appoint the alternative as Prime Minister.