South Yorkshire Police are to hold a press conference at 4pm after a missing 14-year-old Lorna Vickerage was found at Euston train station in London.
John Bush, 35, has been arrested on suspicion of child abduction.
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The MP died at the age of 84 on Sunday.
He held several shadow cabinet posts during his parliamentary career, but had not been active in the Commons in recent months.
Campaigners say that the Government should continue to pay for the scheme.