Jurassic limestones here in northern France do have very long sub-horizontal cave systems.
Normandy chalk possesses some dye-tested karsts up to 28km long (as the crow flies). But as yet the longest cave penetrable is about 2km. (The big problem in Normandy is sediment-fills from the loess soil cover).
So look again a bit harder.... as lincolnshire may have less of a sediment problem.....
If you have sinks and risings, then you can ignore the pessimists !