This is a 'penny lick' glass. In the days before edible cones or cornets, ice cream was served in small glass cups.
These were filled with a pennyworth of ice cream and became known as ‘penny licks.’
When you finished licking your ice cream, you returned the glass. It was (hopefully...) rinsed out for the next customer.
The thick glass made it look like you had more ice cream than you did. This meant there were lots of dissatisfied customers!
It was also unhygienic, as some sellers didn’t wash the glasses between customers. Penny licks were blamed for spreading disease. Because of this, in some places they were banned.
They were replaced by the ice cream cone, which came to the UK from America in the early 20th century.