The B425 is not in central London, as its number might suggest, but in Solihull. Except for the section through Solihull itself, part of the pre-bypass A41, the road was originally unclassified, only gaining its number around 1960.
The first section is Warwick Road southeastward from the junction with the A41 Seven Star Road (at the beginning of the by-pass) to the roundabout junction with Lode Lane (formerly a light-controlled crossroads with some turning restrictions), where it cannons off the B4102 and turns left up Lode Lane past Solihull Hospital. This crosses the A41 at a set of lights and heads north past the Land Rover factory, where there's a brief dualled section. At a roundabout it becomes Hobs Moat Road, which continues past the Solihull Ice Rink and on to Sheldon, where it ends at the busy Wheatsheaf junction with the A45 Coventry Road, notable for the lights on the main A45 all being on gantries above the carriageway.
Thus endeth the brief and not particularly glorious career of the B425.