The Surrey Machinists Company from London was known for the 'Invincible' bicycles. They used this brand name from 1876-1889 for their ordinaries and in later years for the safeties. Very succesful were the 'Invincible' tricycles. The bicycles were high class and often lightweight; Surrey Machinists was succesfull in racing.
A characteristic part, introduced in 1878 (patent december 1877) is their own patent hollow rim.
I have the impression this rim was also sold to other manufacturers. So the Surrey Machinists rim (it has a smal identification plate) doesn't always mean the bicycle was built by the Surrey Machinists Co.
I have never seen serial numbers on Surrey Machinists bicycles.