Boris Johnson lied to the Queen
Boris Johnson lied to the Queen in his request to prorogue parliament. He was not honest in his intentions for doing so, making the move unlawful.
The constitution does not allow a Prime Minister to prorogue parliament for the purpose of stymying debate and bypassing the democratic process.
The prorogation of Parliament, as laid out in the laws and conventions that make up the British constitution, is designed to be used to bring an end to the parliamentary session and outline a new legislative agenda. Because Boris Johnson used the prorogation to stymy debate, it was in breach of the constitution. The primary function of the prorogation had nothing to do with outlining a new agenda and everything to do with stifling democracy.
Parliament is a central pillar of the British legislative process as enshrined in the British constitution. Boris Johnson may prorogue parliament to end the session. However, using prorogation as a mechanism to bypass the democratic process and push the country into a no-deal Brexit is a clear violation of the British constitution. 
Britain does not have a codified constitution. The government is controlled and overseen by a litany of laws and customs that dictate parliamentary behaviour and proceedings. There is no constitutional mechanism that says the prime minister cannot prorogue parliament for as long as he or she deems fit.  Without a codified constitution, Johnson is well within his rights to prorogue parliament, order the Queen to veto anti-Brexit laws, or even invent new public holidays in the run-up to October 31 to prevent parliament from sitting.
[P1] British constitutional norms dictate that parliament may only be prorogued for the purpose of ending the existing session and outlining a new legislative agenda. [P2] Boris Johson prorogued parliament to stymy debate over Brexit. [P3] Therefore, his move was in breach of the UK's constitutional norms.
[Rejecting P3] Breaching constitutional norms is not illegal. There is no codified British constitution. Therefore, there are very few formal limits on executive power.