If the rear hub is a Sturmey Archer three-speed (which looking at the cable it might be) there will be a two digit number preceeded or followed by a single digit number, eg, 74 3 or 3 74 stamped onto it. That will tell you the year and month that the hub was made and provides a good estimate of the age of the bike. In the above example the hub would have been made in March 1974.

I would guess that your bike may be a mid 1970s bike.