From the Wikipedia page on Kilburn 
Kilburn High Road is the main road in Kilburn. It follows a part of the line of the Roman route, Iter III in the Antonine Itinerary, which later took the Anglo-Saxon name Watling Street. This was based on an earlier Celtic route from Verlamion to Durovernum Cantiacorum, modern day St Albans and Canterbury.
Running roughly north-west to south-east, it forms the boundary between the London Borough of Camden to the east and London Borough of Brent to the west. It is the section of the Edgware Road (itself part of the A5) between Shoot Up Hill and Maida Vale.
There are three railway stations on Kilburn High Road: Kilburn Station (Jubilee Line) at its northern end and a little to the south Brondesbury Station (London Overground on the North London Line). Approximately 1.25 km (nearly a mile) further south is Kilburn High Road Station (also London Overground, on the Watford DC Line). Kilburn Park Station, on the Bakerloo Line, lies a little west of the southern end of the High Road.
The green space of Kilburn Grange Park is located to the east side of Kilburn High Road.
The name of Ian Dury's first band, Kilburn & the High Roads, refers to this road, as does the Flogging Molly song, "Kilburn High Road" and the Shack song, "Kilburn High Road".