The Borough of Runnymede is a local government district with borough status in Surrey, England. Its council is based in Addlestone and the borough also includes the towns of Chertsey and Egham. The borough is named after Runnymede, a water meadow on the banks of the River Thames near Egham, which is connected with the sealing of Magna …The Borough of Runnymede is a local government district with borough status in Surrey, England. Its council is based in Addlestone and the borough also includes the towns of Chertsey and Egham. The borough is named after Runnymede, a water meadow on the banks of the River Thames near Egham, which is connected with the sealing of Magna Carta by King John in 1215.