The Bure Valley Railway operates steam trains between Aylsham and Wroxham.
On October 6, one grandparent can travel for free with the purchase of a full-fare adult ticket.
Return tickets cost £22 for adults, £11 for children and under 5s ride for free.
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The 18-mile round trip runs through the pretty Bure Valley countryside, following the meandering River Bure through meadowland and ancient pasture.
Make the day even more special by pre-booking afternoon tea at the Whistlestop Café at Aylsham Station for £15pp.
Pre-booking is essential at bvrw.co.uk or call 01263 733858 (limited to one free grandparent ticket per booking).