A bumper was the name given to a glass, tankard or cup, filled to the brim; throttle is an old-fashioned word for the throat or the gullet.
London society of the Georgian period was renowned for its heavy consumption of alcohol. Poor people tended to drink beer or gin, but a wider range of alcoholic drinks was available to the rich. These included wines such as French claret; fortified wines such as sherry, port or Madeira; and spirits such as brandy and rum. It is noted in the text that Mr Stryver and Sydney Carton have wine, brandy, rum, sugar and lemons with which to concoct their punch.
During the Georgian period, beer might be drunk from pewter tankards, and other drinks, from glass goblets or tumblers.
Click here to see some 18th century pewter tankards and measures.