Stockport Metropolitan Borough Council currently lists the B5423 as being constituted by Prince's Street in Stockport town centre – although its precise co-ordinates as a Class II route are unclear, since less than 200 m of this street remain as a through route for vehicular traffic. The greater part of the street is today either fully pedestrianized or converted to short access stubs for loading and unloading purposes. Certainly the road is not marked on maps.
Prince's Street had first been classified, in the 1922 numbering scheme, as the B6168. It gained its present name, incidentally, only in 1908 (in commemoration of a visit to Stockport by the Prince and Princess of Wales); before that it had been regarded as the town end of Heaton Lane, the road running from the middle of Stockport westward towards the four Heatons (Moor, Chapel, Norris, and Mersey).
By 1939, if not earlier, Heaton Lane – together with Travis Brow to its west and part of Didsbury Road beyond that, as well as the now separately named Prince's Street to its east – had become part of a rather longer B5423 than the stub which remains to us today. The B5423 at that time began at the point between Heaton Mersey and Heaton Norris where the B5169 from Didsbury to Reddish turned left into Bank Hall Road (this is, as it happens, where today's B5169 starts) and ran eastward for 2.3 km to meet the original route of the A626 through Stockport at the Tiviot Dales / Bridge Street junction.
Today the section from the Bank Hall Road turn to the roundabout junction with the A560 – north of the King Street West Bridge (originally known as the Mersey Bridge) and west of the railway viaduct – is a part of the A5145, the alignment of its final 800 m or so having been somewhat shifted by the arrival of the M60.