It’s a fairly common Spear & Jackson.
Mid 1950’s – Mid 1960’s.

The last of the UK mass-produced wooden-handled Sheffield-steel saws, before saw manufacturing went downhill. A middle market saw. Not as highly regarded or collectable as some, but much better than the plastic handled or throw-away saws which came later. You’ll be able to resharpen it and have a perfectly good saw for years to come.
I own three, all about 1963-1967.

Your contoured handle recess was later changed for a straighter shape.
S&J Medallions were replaced with a sticky label.
Some had embossed lettering on the handle.

Your saw nuts are probably one-way push-fit rivets. Don’t try to remove them. It’ll destroy the wood and/or rivet. You can sometimes tap them tighter if they’re loose. Use a wooden dowell on both sides to prevent maring the rivet.

The medallion is probably the screw-in type. Go gently. The threads are fine and fragile and they’re often rusted underneath. I removed my medallions, sanded around the rivets, then refinished the handles.

I also removed the sharp edges with a spokeshave & file to make the handle more comfortable.