There is a Wood Farm on the edge of Flitwick Wood, in the parish of Flitwick but right on the border with Steppingley parish. This appears to still be a farm - the Royal Mail gives its address as:
J. Heywood Ltd, Wood Farm, Flitwick, Bedford, MK45 5WF
However, it isn't listed on
www.imagesofengland.co.uk suggesting it isn't a listed building - this perhaps implies that it's been rebuilt in more recent times. Certainly the Mid Bedfordshire District Council website shows that Wood Farm Cottage next door obtained planning permission to be rebuilt in 1999 following fire damage.
Hope that helps.
Richard.