What plans?
If they bought a field and a barn, the plans would show the field and the barn.
If they bought a field and a barn with the intention of carrying out development which relied on being able to have free and unfettered access to do wotk on land which they were not buying how would that affect the plans for the field and barn which they were buying?
I would expect that if they were charging to provide the service of transferring a legal title/ownership to/of real property from one person to another then they would have the appropriate skills.
But then I would also expect someone who buys land and property not to just assume that he would necessarily have free unfettered access to land which he did not own in order to do things to that land for his own benefit.
The op.said the plans which were made by the farmer and the architect and whoever else is involved, showed the drainage etc.
One would expect that these plans or whatever the op called them would show boundaries and the drainage not in the land being sold.
At the very least it is a question the conveyancer's should perhaps ask as looking out for the best interests of there clients.
As part of the documents the conveyancer would do, a drainage check is part of the standard searches pack. With this they would or should say, where's the drainage? And then check out all the paperwork to see if there are any provision made. Then go back to the vendors conveyancer and say, there doesn't appear to be provision for drainage, and then depending on what comes back and what they see in the paperwork handed over tell their client there is no drainage and you need to get an agreement in place.
No doubt there are many if's and buts and hiding behind legal texts etc etc.
But there appears to have been assumptions by both the purchaser and their conveyancer which has got them in a spot of bother.
and on top of that they have also ended up with, what seems to be a sly farmer who has seen an opportunity to garner more cash.
But as has been alluded to maybe the attitude of the purchaser towards the farmer has played some part of it, and I presume it is because they are angry and upset and feel hoodwinked with no one to turn to.
I'd probably feel the same if I was silly enough not to get a structural report done on a derelict barn and assumed the conveyancer would do their job correctly. ( I personally wouldn't do either)