Family Era/Pre_Transition:
Barling's Make in block lettering with the word "Barling's" arched over the word, "Make". Size stamps run from SS to EXEXEL. If there is a model number it is either a 1, 2, or 3 digit number for the American market or a 4 digit number beginning with the number 1 for the British market.
The exceptions to the block lettered Logo are the Guinea Grain, which has a script "Barling's" with an apostrophe and an "s", and early filtered pipes like the "Pipelet" and the "Cyg-Smoker" which have a script logo.
There is also a short run "Barling's Make" block lettered logo with four digit numbers whose first digit ranges from 2 thru 6, that was produced for a few months in 1962.
Corporate Era/Transition-Post Transition:
The log is a script "Barling" no apostrophe and no "s". Initially the model numbers are all four digits with the first digit ranging from 2 thru 6, and the occasional 7. Later the number 1 comes into use.
You have a Family Era Barling, probably post WW2. If there is a reg'd number stamped on the underside of the stem it was made between 1939 and 1950. The EXEXEL size didn't exist before 1939 and the patent ran out in 1950. If the stem has the words "Barling Design" on the underside, then the pipe dates from 1950-1962.
The pipe appears to have been spared the tender ministrations of a buffing machine. The rim is in rough shape. The logo stamps on the stem appear to have been worn off or barely visible. Value is around $200, more or less, in its current condition. Restored it could be worth a bit more.