A Brief History of the Marque
Peerless motorcycles made between 1902 & 1908 were built by Bradbury in Oldham, Lancashire and were very similar to the standard Bradbury machines with the exception of the engine. They were fitted with 2hp & 2 ½hp Birch engines made under license, with the crankcase cast around the frame tubes.
Leon Mitchel discusses the Bradbury Peerless at some length: earlymotor.com
David Best's Bradbury Pages: seeBritish Resources
A later machine with the name "Peerless" was produced by the International Mfg. Co. Ltd in the years 1913-1914 using Veloce engines.
At least two other companies used the Peerless marque, one in the United States and the other built by Healings in Victoria, Australia. There was also a Peerless cyclecar built around 1914.
Sources: Tragatsch p248, et al.