From the Wikipedia page 
East Barnet was a local government district in south Hertfordshire from 1863 to 1965 around the town of East Barnet.
The district was created under the Local Government Act 1858 on September 25, 1863, as East Barnet Valley Local Government District. The district was governed by a local board. Apart from the parish of East Barnet, the local board's area included surrounding areas of the parishes of Chipping Barnet in Hertfordshire and Enfield, Monken Hadley and South Mimms in Middlesex.
In 1889 the boundary between Hertfordshire and Middlesex was altered by the Local Government Act 1888, so that East Barnet Valley was entirely in the former county.
The Local Government Act 1894 reconstituted the local board's area as an urban district, governed by East Barnet Valley Urban District Council. The urban district consisted of three civil parishes, shown below with their area in 1901:
East Barnet (1,697 acres) Barnet Vale (the area formerly in Chipping Barnet parish) (279 acres) Monken Hadley (the parts formerly in Middlesex) (668 acres) The urban district was renamed East Barnet in 1935.
The district formed part of a long, thin protrusion into Middlesex and was surrounded by that county on three sides; to the north, east and south.
The urban district council adopted an unofficial coat of arms consisting of a shield bearing crossed swords between a red rose of Lancaster and a white rose of York and the Greek letter omega. This design represented the Battle of Barnet, the final battle in the Wars of the Roses. The chief or top third of the shield showed a fleur de lys between two flory crosses, emblems of St Mary, the patron saint of the ancient parish of East Barnet. In 1955 this became the basis for an official grant from the College of Arms. A crest was added above the shield: a hart from the arms of Hertfordshire County Council, with a shield hanging from the neck bearing the cross of St Alban for the historical associations of the Abbey of St Albans with the area. The motto adopted: Willingness Rids Way, was from Shakespeare's Henry VI, Part 3. It comes from a speech made by Edward IV following the Battle of Barnet.
In 1965 the urban district was abolished by the London Government Act 1963 and its former area transferred from Hertfordshire to Greater London . Its former area was combined with that of other districts to form the present-day London Borough of Barnet.