Practical advice there, Dougal. As a few have suggested, the filled in ditch sounds like the reason the field drains poorly - sorting out that problem, whether it's your ditch or the councils, sounds like a perfectly proper thing to do.
If the council ever decide to look into the fence line and (re)claim the ditch, as Dougal says, keeping it clear then becomes their problem - but most landowners would still clear the council ditch if it was causing waterlogging on their own ground.
Hereabouts it seems that the verge is owned by and the responsibility of the landowner but the council and utilities seem to have rights to dig into the verges (and not replace the landowners daffodils, apparently
) if needed. Maybe it's an England / Scotland difference?