Speaking to ITV News, Virgin Train has confirmed: "Both lines to Manchester are now open. Services are beginning to run, but delays will continue for the time being"
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Ionut Gheorghe, 27, was detained in Los Molinos near Madrid on Friday by Spanish police under a European Arrest Warrant.
Barrie died at his home in Uxbridge, west London, after a short battle with cancer.
The first of the 66 trains for the recently-named Elizabeth Line was unveiled at a factory in Derby.