Green’s Dictionary of Slang

hearth-rug n.

[rhy. sl.]

1. a fool, a simpleton [= mug n.1 (2a)].

[UK]R. Puxley Fresh Rabbit.

2. a drinking mug.

[UK]Dodson & Saczek Dict. of Cockney Rhy. Sl.

3. a bedbug.

[UK] (ref. to 1930s) R. Barnes Coronation Cups and Jam Jars 57: They were also known as Hearth Rugs, or Steam Tugs to the well-initiated.
[UK]R. Puxley Fresh Rabbit.