Covent Garden index
Existed from at least 1787. This looks like it is Bow street Police station by 1842, and maybe a lot earlier. This was apparently built in 1831-32 according to history online, where they remained until 1880, when it moved to its present building by the magistrates court. Incidentally, in 1830, the Brown Bear is described as opposite the Police station, but this is clearly an earlier police office, if describing it as such before the building of the current police station.
A note to add to this, I have found an excellent picture of the Brown Bear, dated 1825, showing Hazard as the licensee. The picture is described as opposite the police station, but the picture is annotated as 'now the police station.
A listing of historical London public houses, Taverns, Inns, Beer Houses and Hotels in Covent Garden - St Pauls, London.
You may also wish to take a look at the St Clements Danes parish.
Residents at this address.
1787/John Foreman, victualler, Brown Bear, Bow Street, Covent garden/../../Sun
Fire Insurance - access to archives
1805/George Hazard, Brown Bear, Bow Street, Covent garden/../../Holdens Directory
[In 1832, there is a George Hazard at 3 London wall, which is a coffee rooms in 1842, maybe earlier ]
1825/Mr Chaffey, Brown Bear, Bow street, Covent garden/../../Licensed Victuallers Association
1829/Charles Attwood, Brown Bear, 33 & 34 Bow Street//../../Pigots Directory