My wifes gunna kill me!

[Illaveago]

I found a 1951 BSA New Hudson Silver Arrow on a web site with which you may be able to compare a few details with . I found it just by looking at head badges. The badge on that cycle was circular whereas yours has bits added on to the bottom more like the original ones. This may mean that yours pre dates that one.

 

[Illaveago]

Did a bit more looking! At that time they were advertising them with BSA 3or 4 rear hubs. The lugs look similar to yours.
The position of the badge fixing holes also changed from horizontal to vertical and from being fancy pressed brass to plain flat painted.
There are some adverts from 1936 which also show a model similar to yours stating that certain fixings like pump brackets were brazed on.
I seem to have widened the field a bit ! It seems likely to fit in the time from the BSA takeover to the 50's.