I lived at Longborough for a year, so know the area pretty well. Shame about no car, as there are some corkers for an evening walk a little further afield.
Anyway, Wolford Wood is nice. You say about a mile east of MitM, so I'm guessing the Fire Service technical College, or thereabouts. That would mean Lemington Heath Coppice, Wolford Wood, Great Wolford (nice earthworks if like me you're into archaeology), Barton-on-the-Heath and back. A little over 5km, but cut-shortable.
Might be a bit far, but you can get up onto the hill at Wheelbarrow Castle for good views.