In that case if it has a CPH or not won't matter. Even if it hasn't and you later decide you want livestock it isn't hard to get a holding number. Just avoid looking at anywhere with an AOC.
Round here the price of places with any land is higher because it's in demand by the horsey brigade.
You might also want to check what planning category the land is. For example, my field is not part of my garden, even though they are one property. Thus I cannot lawfully grow vegetables in it, or keep pet sheep in it, or actually put up a swing. I could lawfully graze meat animals or grow vegetables to sell in it, because that is agriculture and not classed as development. I can't keep horses in it, because horses have their own special planning category, unless they are actually draught animals.
It sounds petty and pedantic, and planning won't bother you unless you do something provocative, like put up a polutunnel (which you might want to do) or the neighbours complain. Which they might. Neighbours can be horribly petty, especially if the people before you weren't very considerate.
I think what you need to look for is 'use ancillary to the enjoyment of the dwelling house' Avoid 'open countryside' (which is what mine supposedly is) or agricultural, unless you are planning on selling stuff.
Like Nick said, registered is fictional. Planning, sadly isn't.
||You might also want to check what planning category the land is.|