I did wonder myself where that estimate made by Patrick Vallance had come from.
Obviously, the government's advisers will probably have access to a range of data sources that haven't yet been made public. However, my instinct is that they've basically undertaken a fairly simplistic extrapolation of the current new cases trend.
If you look at the daily confirmed case statistics, as of a couple of days ago, they were doubling pretty much every 14 days. If you roll that rate forward, it would take 52 days from two days ago to reach 49,000 cases per day, which would take us to 11 November.
However, some of the current rate of increase is accounted for by the ongoing increase in daily tests processed (it would a much more straighforward comparison if the government would release daily stats for the number of people tested). This data suggests that an increase in cases of around 33% would be expected every 14 days, due to increased testing.
What this means mathematically is that the 'real terms' increase in cases every 14 days is approximately 50%. On that basis, numbers would double in real terms every 24 days.
Presuming that both those trends continue, In order to get from the current 7-day average to an average of 49,000 new cases per day (in real terms) would take 90 days. This would take us to 19 December - just in time for Christmas!