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We will be  staying at Belton Woods and Mrs Zip wants to do National Trust type stuff which gets me a free day.
Is there any biking nearby?
A google shows lots of beautiful singletrack but thats Grantham New Hampshire.
There's some bridleways over towards Belvoir Castle.... http://www.mountainbikerides.co.uk/routes/2-leicestershire/4-belvoir-loop.html
Vale of Belvoir is OK, although likely to be a mud fest at present.
I moved away a couple of years ago or I'd offer to show you around. It's more pretty bridleways than massive gnar, or whatever the phrase is.
Sherwood isn't too much of a drive if you have the time and a car, pleasant enough but their red grade wouldn't make blue up here.
Do you ride road? That's very big in that neck of the woods, for obvious reasons, and if you are competitive their are some very fast time trial courses. Plenty of friendly clubs nearby so you could tag along on a cub run, Sleaford Wheelers were mine, but Witham are nice chaps too.
Lack.of MTB was one of the reasons I moved, now 20 miles from Peebles and the hill out of my village is twice as big as Lincolnshire's highest!