The first one is for the well-known luxury car manufacturer: Jaguar. It seems the winged logo was used for about a decade after the Second World War.
Something was written under the logo. It ends in '..an' but the rest has faded too much.
The second sign is for what was certainly a corner shop.
...arettes [Cigarettes] ....
Location: Crescent Lane, Bath, Wiltshire / Picture taken on: 17/07/2010