I'm in this positition and I know people will tell me off, but I am working on a don't ask don't tell basis.
Yes, my business is registered at this address, but I hold only a couple hundred quids worth of stuff here (no clients at all) and I don't plan on any funny business. When I move the first call I will make will be to HMRC is changing my address. If I thought I was going to get into any trouble with my business I would close it down/change address rather than risk damaging the credit rating on this address.
I have asked my insurer about this, and they said that it made no difference to them. However if my business caused any problems I would be liable. But I assumed and expected that anyway.
To be honest, my understanding is that those rules are standard in tenency agreements to stop landlords becoming liable for changing the purpose of the building ie. they could get in trouble if you turned the place into a cafe or shop. Planning law would mean the landlord would get into trouble in this situation. However, if you don't chnage the purpose of the dwelling (you are living in all of it) then I don't think that those laws are invoked. You don't pay business rates for example do you?
I wouldn't say anything to the estate agent myself, but maybe you are more honest than me. I just really don't see what it would gain, and fail to beleive that no tenents across the country are self employed.