The ever-useful Underground Map gives "Kilburn Bridge once marked the spot where the Edgware Road crossed the River Westbourne. Kilburn Bridge, which was recorded in 1398 and thought to have been built in the mid 13th century by the prior of Kilburn, carried Edgware Road across the Kilburn brook (the Westbourne River). In 1826 the original stone bridge with a Gothic arch survived, flanked by brick portions added at two different periods.By that date repair was shared between the trustees of Marylebone turnpike and of the Kilburn Road. In more modern times, as the river has been culverted and sent underground, there is no trace of the structure."
This location for the bridge is supported by the 1836 'Plan of the parish of PADDINGTON in the County of Middlesex 7' which shows a river, the 'Bayswater Rivulet' crossing Kilburn High Road here.