Had my covid booster over a month ago and booked the flu jab at the same time for 8 Dec.
I won't have a privilege getting it as I'm over 50 and on the CV list, my GP always makes sure there are enough for those of us who are CV and have it every year, even if we choose to have it late.
I remember being told years ago when I worked for the NHS and a nurse came into our offices in late Nov, that the vaccine only works for about 3 months and with the worst of the flu season usually being Jan and Feb, it's best to have the vaccination later than earlier.
Also, just a quick thinking point.... for those who may have side effects from either the covid or flu jabs, if you have them both at the same time then suffer side effects, apart from a sore arm (each jab done in separate arm) how will you know which vaccine caused the issue? Another reason to consider having them done at least a week apart.