I was on eBay and I found a white Brodie helmet, who might have worn it? It looks like this https://images.app.goo.gl/NXLymAZpLKKuL4E67
It doesn't have any readily visible markings but white helmets were used by various civil defence bodies in Britain both during and after WW2. In particular, they were worn by ARP wardens (typically marked with a W) or fire wardens (typically marked with FG), specially designated rescue parties (R), or repair parties (RP).
A contemporary identification guide can be seen here.