Hi
@Danz,
welcome to the Cabe, good to see another person from the UK on here, there aren't many of us!
Some interesting and informative posts have been made above.
It can be very hard to identify British bikes from this period as there were still so many manufacturers, and even more marques.
As
@ccmerz said above it looks like a Sunbeam, and it certainly does, bit I don't have the expertise to be 100% certain.
It's definitely very similar to a ladies bike from the period that I have, that I believe to be a Sunbeam also.
Regarding the rear hub, try an internet search for ' K series S-A hubs'; it should lead you to a pdf by the world expert on S-A hubs Tony Hadland. This could help with dating your machine.
The frame number is the one on your seat lug.
The number under the bottom bracket is the casting number for that lug.
I would thoroughly recommend joining the VC-C in the UK (The Veteran Cycle-Club) if you are into older bikes.
Not only for the amazing magazines and literature available, but also the wealth of knowledge, the invaluable online library, friendly people and regular rides that they organise all over the UK (when lockdown restrictions are lifted of course).
There are several London groups within the club and they are pretty active on the riding front.
Don't worry about the strange looks you've been getting, you will get used to them, eventually!