I assume you're looking at a freehold purchase? If leasehold, things will be more complicated still.
A covenant can run with the land, or it may be a personal covenant. Either way they can appear in the land registry particulars: see
here.
My understanding is that negative covenants (not to do X) are more likely to persist through change of ownership ('run with the land') than positive covenants (e.g., to pay over 12.5% of earnings from the plot). That's because the common law, reasonably enough, makes it hard to commit future owners to a contract they weren't party to. But it's not impossible.
I think you need to look very precisely at what the covenant says: it will be a covenant to DO
x or NOT TO DO
y. That is what can be enforced in law. Your words "they retain the right towards 12 1/2 % of any earnings gained from the specific area" do not express a covenant that I recognise. The right they have is either to DO something on the land themselves (eg, graze their sheep over 12.5% of the area, or collect 12.5% of the apples on the trees) or else to sue you in court to make you DO something: eg, TO PAY £
v calculated by formula
w.
Then the question is whether that covenant runs with the land, such that you will be liable to it qua freeholder of the property, or whether it will die on change of ownership. The guidelines on privity linked above may help, although you'll probably need to know exactly who were the parties to the relevant sale.
If the covenant will run with the land, then ask who has the benefit of the covenant. Is it benefitting another estate (probably a remnant of the land out of which the parcel containing the pub was carved)? Or is the beneficiary the vendor personally? If it's another estate, there's a high chance the present owner doesn't know they have the benefit - it won't appear in the deeds of their estate, only in yours. If the vendor personally has the benefit, check to see whether it's a company that's dissolved, or a person who's long since passed away, etc.
And then, as the Byre says, the covenant can wither away through non-enforcement even if in other respects you would be liable. If The Byre is right that the covenant grants them 12.5% of the profits a prendre, then they get 12.5% of nothing if you don't grow anything there.
In all cases an insurance policy may be an easy fix - they cost about £15 ime. And/or, depending on the credit of the potential vendor, you could take an indemnity from them as condition of purchase.
But you will need to know exactly what's going on legally first. You'll eventually want a solicitor, but I am in your position regularly - often, bootstrapping the due dil in the early stages will have to do. HTH
