Well, I've been able to solve this myself. I hope the below helps others.
I've discovered that the extension was invoked, but failed to show anything on the shipment drop-down on the cart page for two reasons:
- no location zones had been set up for the location (country) which was selected in the Shipping Extension admin page
- the cost was calculated (correctly or incorrectly) to be zero.
The xx_zones_to_locations table only had entries for the USA, whereas UK entries were essential given that this is a UK-only service, the Royal Mail. I don't know if I had installed Abantecart correctly, but by tinkering directly with the database, I have added 100 entries for UK locations to this table.
I think you can achieve the same result without knowing any SQL by selecting System -> Localization -> Locations. Make sure the country is there, click on the Edit symbol and choose Location Zones. If no zones for this country are shown, click on the plus top left. Select the required country, select all and save. The zones will be added to the 'location'.
I have to say that this ability to choose 'zones' within countries is a very good facility of Abantecart. Without it, getting the charges right for shipping to remote locations would not be possible.
However, this was not enough to bring up the shipping in the shipment drop-down.
In addition to this, references in the code to weight units were incorrect, the string literals should end in ..._class not ..._class_id. This meant that weights in grams were not converted to kilograms, so the code tried to find a charge for a weight of hundreds of kilograms! No surprisingly this failed, the maximum weight being 1 kilogram, and so a cost of zero was 'calculated'. When the weight classes were corrected, the shipping offer appeared in the shipment drop-down. Success.
I attach the corrected php file.