Rumbelows was a white goods store, so didn't sell medicines. I think some of the symbols may refer to duplicate items. I'll give you my guesses using the letter above to refer to the symbol.

The R, U, and L symbols are all from a tape deck, and are play, stop, and pause respectively. The M is a roll of camera film. The B is a frost symbol, and most likely represents fridges / freezers. The E is an on/off symbol; it may just refer to generic electrical equipment, or could possibly represent cookers. I have no idea what the O and W are supposed to be, but if I had to make a stab in the dark I would say one may be microwave ovens and one may be radio or TV. The S is most likely washing machines, as someone else has mentioned.

They were a UK electronics retailer. There's a wiki article with some info: https://en.wikipedia.org/wiki/Rumbelows

Sadly, it doesn't touch on the symbols of the logo

The frost icon is likely freezers, and the spiral is laundry washing machines