The UK does not have a codified constitution, leaving very few formal restrictions on executive power.
Without a codified constitution, there are almost no formal restraints on Boris Johnson’s power, leaving him free to prorogue parliament when and for whatever length he sees fit.
The British Government, unlike many other national legislative bodies, does not have a single, written, codified constitution which outlines inviolable limits on a leader’s powers. Instead, the government functions by everyone adhering to a loose set of laws and customs. Providing everyone adheres to these conventions, this works. But Brexit is testing the limits of the constitution. These are unconventional times and flexible, unconventional solutions are required to deliver Brexit. It may be difficult for MPs to accept that the prime minister has decided to prorogue parliament in the run-up to Brexit, but there is no formal restriction preventing him from doing so.  This is the beauty of having an uncodified constitution. It possesses the flexibility to allow for the novel, unconventional solutions to unique and pressing problems, like those associated with extracting Britain from the European Union.
Instead of a codified constitution, the British government relies on a network of laws and conventions to place checks and balances on executive power. Conventions form the backbone of parliamentary proceedings. They are, after all, the source of Boris Johnson’s prime ministerial authority. Convention dictates that the prime minister is the person that commands the authority of the Commons, either as the majority party leader or the head of a coalition.  There are two implications for this. Firstly, if Boris Johnson wants to do away with parliamentary convention, then he will have to find an alternate source of power as prime minister. He cannot accept parliamentary conventions when they suit him and discard them when they do not. Secondly, because parliamentary conventions (along with laws) make up Britain’s uncodified constitution, breaking parliamentary convention is tantamount to breaching the British constitution. Therefore, in proroguing parliament for an unprecedented period of time, Johnson has violated the constitution, making the act unlawful.
[P1] There is no written constitution in the UK. [P2] This means there is no constitutional violation in proroguing parliament for the length of time Boris Johnson has. [P3] Therefore, his prorogation was entirely legal.
[Rejectin P1] Just because there is not a written constitution doesn't mean there is no constitution. The constitution is constructed through acts of parliament and conventions. [Rejecting P2] Therefore, violating parliamentary convention is tantamount to violating the British constitution. [Rejecting P3] Boris Johnson's prorogation violated convention both in its length and its motives. Therefore, it violated the British constitution. Therefore, it was not legal.