Rapid are based in Colchester and do a wide range of components but they have no shops. Farnell tend to supply high-quality components to designers but again have no shops. They are based in Leeds. Both have a local trade counter.
NR Bardwell have a mail order business and a shop in Sheffield. It stocks a wide range of electrical, electromechanical and electronic requisites and the shop is worth a visit just for the quality of the service you get.
Much the same as the above can be said of Bowood, which is in Chesterfield. Mainly internet orders but trade is welcome Monday to Friday in office hours.
Oomlout is the definitive site for those of you who wish to master the Arduino system for microprocessors.