This might be more definitive:
> Google "how close can livestock be to dwellings"
> Scroll down to the 7th result "PDF Report - Local Government Ombudsman"
> Check out item 12 on Page 6, which states the following:
12. An agricultural building of less than 465sq m on a 1 hectare plot within a 5
hectare field can be built without applying for planning permission (i.e. is
permitted development) if it is not used for housing livestock within 400m of the
curtilage of residential dwellings. (The 400m zone is widely referred to as the
‘cordon sanitaire’.) Planning permission is needed to erect agricultural buildings
within the ‘cordon sanitaire’.
"Cordon sanitaire" would appear to be your starter for ten.
ETA: Idly wondering if kcg would worry about cows next door ...