Ursula62 is also correct in saying that having part of your house used for business purposes means that you may have to pay business rates. You can, however, offset this against tax by charging your business 'rent' for the use of space in your home.
It's also worth noting that your property and contents insurance might be invalidated if you don't tell your insurer that the house is used for business purposes.
Having written all this, however, it's worth looking at what type of business you are planning to run from home. The legislation and insurance restrictions theoretically apply to all types of business but it's unlikely that someone who was simply using their home address as a base for a service (e.g. a plumber) would encounter any problems.
If you're planning to operate a business that involves you keeping small amounts of stock on the premises (e.g. those people who visit workplaces offering jewellery or cosmetics) then you ought to think about the implications for your insurance policies but it's unlikely that the local council (or anyone else who has an interest in a covenant) would be bothered about this.
The real problems that are likely to arise come from those types of business which involve customers visiting your premises, delivery vehicles frequently parking outside your house or advertising signs being placed on the building.
Returning to covenants, remember that they're basically put in place to maintain certain standards in an area but, as long as nobody objects, the terms of the covenants are never invoked. (My house, in South Suffolk - just up the road from you - has, like all other houses on the estate, a covenant prohibiting external TV aerials. This is a really poor area for TV reception and every house on the estate has an external TV aerial! The message here is that covenants can, with discretion, be ignored as long as nobody complains!).
Chris.