Hello and welcome to the forum. Whereabouts in the UK are you?
As far as I'm aware, with regard to planning, in this country you can do pretty much as you like until someone complains, Keep the noise down and make sure that you don't generate too much extra traffic. Don't light a coal forge when the neighbours have washing on the line! I have no idea if this applies in urban areas, I would imagine that life is less pleasant in such places; I try to avoid them!
The domestic building regulations are concerned with fireproofing and ventilation and are really just common sense. Here is one of most relevant; http://www.planningportal.gov.uk/uploads/br/BR_PDF_ADJ_2002.pdf
It's best not to get local authorities involved if possible as they tend to get over-excited about things like compressed gasses, pollution and waste disposal (they can charge for it). They can also hit you for business rates.
By the way, you may not be aware that you need the proper certificates etc. to work as a farrier. This is enthusiastically enforced; you will be caught if you break the rules.