Disruption on East Coast between Kings Cross and Berwick-upon-Tweed, and between Kings Cross and Leeds due to adverse weather conditions.
Tickets being accepted on First Capital Connect, First Hull Trains and Grand Central services.
Northbound trains between York and Darlington are subject to delays of up to 40 minutes.
All other East Coast services in England are liable to delays of up to 30 minutes.
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72-year-old Arthur Bierton from Thirsk was convicted at Teesside Crown Court of abusing two young girls in the 1980s and 90s.