If I understand you correctly, it would be a "½ Penny Lanarkshire (Token) - Glasgow / G. Shearer" if it was DH#2.
However, it is lighter and smaller than DH#2, so perhaps it is DH #3 (especially with the “PAYABLE IN LONDON” edge lettering).
In addition to the above, the token appears to have been struck approximately 15% “off center” (an estimate I made without the use of measuring devices …).
I do not have “DH” available so perhaps a learned numismatist that has access can confirm that; a) there is a DH #3 listing and b) that there is no corresponding Numista listing, which would mean that I could create one.
Cheers
"EVERY COIN IS CLEANED. CLEANING, THEREFORE, IS ALWAYS A MATTER OF DEGREE.
If you send a "dirty" coin into a grading service to be "conserved" and let them do the "conserving" they will charge you for their work CLEANING the coin ..."