The B4513 ran though Old Hill, a locality now in the metropolitan borough of Sandwell in the Black Country, roughly equidistant between Dudley, Halesowen, Stourbridge, and Oldbury. Owing to the road's short length its history is not fully known but it had definitely gained its number by the mid-1950s. The road connected the A4100 Reddal Hill Road to the A459 Halesowen Road, but lost most of this linking function when the A459 was realigned to bypass the centre of Old Hill at the end of the 1980s.
Many maps show the B4513 retaining its Class II status for a number of years nevertheless, and ending, curiously, at a junction with the by-then-declassified Halesowen Road next to Holy Trinity church in Old Hill. The route of the first 200 m of the B4513's western end was also changed latterly so that it followed the whole length of Lawrence Lane instead of leaving Reddal Hill Road by way of the straighter – but somewhat narrower – Claremont Street.
