In September 1944 the ME 262 would have the Meteor for breakfast. With a 100mph speed advantage they can control the engagement from start to finish (provided the engines didn't burn out), and they are all flown by specially chosen experts.
I have strong doubts about that, even though my previous post referred to the more likely frametime for an engagement, spring 1945.
In September 1944 there is that speed gap, yes. So what? Assuming the ideal level field conditions proposed in the OP, both fighters turn to face the enemy and start accelerating from cruise speed, because both are bad at quick acceleration and therefore both pilots decide they need to bank speed.
So you have a first ballistic contact in which the combined speed is such that the two targets are in range of each other for a small fraction of a second - chances are both pilots miss.
And then? As mentioned, both fighters are bad at real dogfighting because they are as maneuverable as a 18-wheeler, and all the more so at top speed. With equally skilled pilots, they can probably only achieve another frontal pass - with probably the same result. The speed advantage would count only if the Meteor decides to break contact first, which is unlikely both for strategic reason and because this fact would be obvious to the British pilot too.