Longbridge had two.
Both were Davenports, so not quite the same as the SR ones.
Locomotive Type Manufacturer Built Works No Acquired Disposal
Ada II 0-6-0T Davenport Locomotive Works, Iowa 1943 2503 1947 from USATC Scrapped 1957
No, 5 0-6-0T Davenport Locomotive Works, Iowa 1943 2505 1949 from Morris Nuffield Works Scrapped 1958
Information from http://www.warwickshirerailways.com/misc/austin-motors.htm
There is a picture of No. 5 near Longbridge East box in Roger Shenton's book 'Changing Tracks' and a picture of one carrying the number WD1938 reputedly shunting at Longbridge also exists. From the lists available on the net this would correspond with the USATC number for Davenport 2503.