Without doing any research, I would suspect the label might not be that much help in identification. I the heyday of banjos and banjo bodied "other" instruments such as mandolin and uke, there were a lot of instruments sold with labels added by the shop which sold them. A number of manufacturers made mass production models for sale to the music shop trade or sometimes a specific design made to order. They didn't badge such instruments with their own trade mark, that was done further down the line by the sellers.
Once again, without any research, the fact that the label says British Manufacture would suggest to me that it may have been made for export.
Of course all that is just speculation. It helps identification if we can see a picture of the instrument. Often people with similar queries have given a link to a photo on their web site or a picture sharing site such as flickr or photobucket. Sometimes the shape or design can be a dead giveaway to the maker, if not the seller.

I am a 5-string banjo player, not uke, but the "bulk" manufacturers made a variety of different instruments. Maybe someone with better ideas will come along, but that is my best suggestion.
Quack!
Geoff the Duck.