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In page British Rail Class 81:

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Because they were restricted to those lines electrified at 25 kV AC they only operated on the West Coast Main Line. Cities where these engines could be seen included London, Birmingham, Manchester, Liverpool, and Glasgow. They operated passenger trains, freight trains, and parcel trains. There is no record of operation on the Ex-Great Eastern line, which was being electrified at the time of their introduction, nor subsequently on the East Coast Main Line (ECML) when that was electrified in the 1980s.