Obtaining a new car right on the September 1st new registration date is always going to be more difficult than other times of the year (bar the same in March). Dealers do their utmost to flog cars they have in stock around these times & long waiting times for new stock to arrive has been the norm since the Covid pandemic and subsequent chip shortage.
I guess it depends on which part of the country you live too. Cars are easier/quicker to obtain in certain parts of the country than others.