Hi
Yes, there's nothing marked as scheduled in that field but the whole Witham valley is rich in archaeological finds and sites, through prehistoric to medieval. Francis Pryor included the Witham in his book Britain AD and there is also an A4 booklet on the area 'Time and tide, the archaeology of the Witham valley'. I've got a copy but haven't got round to reading it yet but just having a quick flick through shows a plan of the area just to the south of your field with a causeway that looks like it would pass through, or close by, the area you are interested in. There are also plenty of earthworks too but it doesn't make it clear what period these belong to. The plan comes from the 'National Mapping Programme sheet TF 07 SE' if you can find a copy, sounds like the local archaeo and museums are your best bet.
While you're in the area there's a nice barrow about 3-4 miles southeast called King's Hill at TF121707
I'll try and dig out a photo and post it later.

-Chris