Boris Johnson addressed the nation from Downing Street after 6pm after chairing a meeting of the Cabinet.
He said there were "no circumstances" in which he would ask the EU to further delay Brexit.
Mr Johnson said it would "hold us back" if Brussels believed MPs would back a "pointless delay".
He said he was "encouraged by the progress we are making" and the chances of a Brexit deal "are rising".
The statement came ahead of the Commons returning from its summer break tomorrow, when the cross-party alliance of MPs were gearing up to attempt to launch their plan to block a no-deal Brexit.
Mr Johnson argued that there would be "due time" to debate Brexit.
Outside Downing Street, he said: "Five weeks ago I spoke to you on these steps and said this Government was not going to hang around and we would not wait until Brexit Day - October 31 - to deliver on the priorities of the British people.
"I'm proud to say that on Wednesday the Chancellor, Sajid Javid, will set out the most ambitious spending round in more than a decade.
"I said I wanted to make these streets safer and that is why we are recruiting another 20,000 police officers.
"I said I wanted to improve your hospitals and so we are doing 20 new hospital upgrades on top of another £34bn more going into the NHS."
Mr Johnson added: "To push forward this agenda on these and many other fronts then we need to get a Queen's speech in October, while leaving due time to debate Brexit and other matters."
The Prime Minister said he believes talks with Brussels have moved forward in recent weeks because the Government "wants a deal, has a clear vision for the future relationship" and is clear that the UK will leave the EU on October 31 "come what may".