There's no 'yes' or 'no' answer here but I'll do my best to cover the important points:
Let's start with planning permission:
You need planning permission for a 'change of use' of a property or any significant part of it. The local planning department won't be bothered if you simply use your home as a base for working as, say, a plumber or carpenter (unless you store a large quantity of materials at home, thus changing part of it into a 'warehouse'). Similarly, they almost certainly won't be bothered if you simply use a spare bedroom as an office for taking on book-keeping work. However if you intend to use your garage for a car repair business, or you want to convert a room to use as a dog-grooming parlour, you'll almost certainly require planning permission.
The next consideration is business rates but the same criteria as above would probably apply. i.e. you'd need to pay business rates (as well as council tax) if you used your garage for car repairs (or a room for dog grooming) but you'd probably not need to do so simply because you used a spare bedroom as an office.
Then there are restrictions imposed by mortgage lenders or (for rented properties) landlords, to be considered. They normally state that you can't run a business from the property but, once again, the nature of any business would need to be taken into consideration. It's extremely unlikely that anyone would object to a plumber or carpenter simply taking phone calls at home (or including his home address in advertisements for his services). Someone doing an 'office job' (such as book-keeping) at home would also be unlikely to fall foul of the rules. However any job that involved a'change of use' of part of the property OR which involved clients calling at the property could well breach the terms of the contract with the lender/landlord.
Lastly, it's worth remembering that (irrespective of the nature of the business) it would be wisest to notify an insurer (whether for property or contents insurance) that a business was being conducted from the premises, otherwise a policy might be invalidated.