From the Wikipedia page :
Brentford and Chiswick was a local government district of Middlesex, England from 1927 to 1965.
It was created an urban district in 1927 by a merger of the former area of the Brentford Urban District and the Chiswick Urban District. It gained the status of municipal borough in 1932. It included the parishes of Chiswick, New Brentford and Old Brentford.
In 1965 the municipal borough was abolished and its former area transferred to Greater London to be combined with that of other districts to form the London Borough of Hounslow.
Brentford and Chiswick was also the name of the parliamentary constituency that covered the area. The seat survived until just before the February 1974 general election, when it was expanded westwards and renamed Brentford and Isleworth.