An interesting question, and although I don't know the factual answer I might hazard a guess, based on the following.
When Birmingham Corporation set up a Tramways Department to operate its own trams on lines it owned (and had laid by virtue of 'Corporation Acts of Parliament') in 1904, until then leased to various private operating companies, the man they picked as the first General Manager was Lincolnshire born Alfred Baker, who after starting his career in transport at Nottingham had moved to London where he became Tramways Manager of the London County Council (L.C.C.).
As a new operator, and one financed by the City's Corporation (although in those days the department ran at a profit, which was used to reduce the city's rates bill) his standards were of the highest, and remained so throughout the life of the department.
The existing 'company' trams were green (Birmingham City Tramways Co Ltd, and South Staffordshire Tramways Co Ltd) or dark red (City of Birmingham Tramways Co Ltd) so a different colour was required to define the Corporation's cars from the others - and other than gaudy yellows and pinks, or difficult to keep clean white, the only obvious other colour was Blue.
The actual shades chosen were known as Prussian Blue and Primrose, and as the old paints were mixed with, and later overpainted by heavy oil-based varnishes, the shades appeared darker than they really were, pale yellow and almost black. These colours remained as the fleet livery until the City's transport department passed to the then new West Midlands County Council Passenger Transport Executive (WMPTE) in 1968, when the Prussian Blue, which was not by then a shade covered by the BS (British Standard) colour chart, was changed to a slightly lighter shade.
Now, as to why the Corporation's other vehicles (dustcarts, lorries, etc) and lamp posts (and even the tram wire support poles) were Green - any ideas?