This question intrigued me and I think I found a plausible explanation. Perhaps what you are referring to was originally called a Stepney spare wheel.
The Stepney Spare Wheel was invented by Thomas Morris Davies in Llanelli in 1904. At that time, early motor cars were made without spare wheels, so a puncture was an event dreaded by all drivers. Mr. Davies’s brilliant idea was to make a spokeless wheel rim fitted with an inflated tyre.
Pretty soon T. Morris Davies and his brother Walter were in business, turning out spare wheels in their Llanelli works. They became very wealthy men as their business grew and they set up agencies across the world.
Their 1909 catalogue proudly claimed that Stepney Spare Wheels were fitted to all London taxis. In 1922 the company became Stepney Tyres Ltd and their operations moved from Llanelli to Walthamstow. The days of the patent spare wheel had drawn to a close, as car manufacturers began to provide spare wheels with all new cars. However, the name lived on, long after the last spare wheel was made. A “stepney” is still today the everyday name for a spare wheel in India, Bangladesh, Malta and Brazil, where it is called an “estepe”. A further twist to the tale is that in Dehli an easy going member of staff, who is not much help, can also be called a “stepney”. A photo is available here (with the above text)