Photographing buildings is very complicated and, for commercial work requires you to obtain permission from property owners, fill in risk assessments and have public liability insurance for several million pounds (pretty standard in pro photo insurance policies).
There are other reasons too:
Police and security stopping you as a suspected terrorist
Private security stopping you because you are on private property
Health and safety in busy places and/or when using a tripod.
Private property will often allow individuals to take a few photos hand held as long as you don’t make a nuisance of yourself, say you are an amateur with no interest in selling the photos and you are not using a tripod. If you are professional they usually expect you to fill in some paperwork and pay for a permit. A recent one for the area around New City Hall in London were very helpful and sent me the forms and rules to follow, albeit quite lengthy, for example.
Police were using section 44 of the anti-terrorism act to stop and search photographers until the European Courts told them to stop in 2010 because it was illegal. It has reduced but not stopped them doing this but they must believe that you are a serious terrorist threat now or face a complaint and compensation claim from the harrassed photographer.
If you are commissioned to do building photography then you must include the cost of the permits in the quotation for the job and find out all the property owners to contact for costs to avoid being stung at a later date, or worse, the job having to be delayed or called off. If you are doing speculative photography to go in a picture library then it’s up to the person at each property whether they make a charge.
I avoid taking speculative photographs inside any building because it is obviously private and would involve obtaining permits and usually paying fees. If it is a commission then the client pays these costs.
I have no experience of English Heritage although I suspect I have taken pictures of some of their properties, if it’s obvious I tend not to take the photo.
The National Trust is becoming very restrictive. They always prohibited photography inside properties but now they are stopping professional photography anywhere on their land. Since they own so much of the UK, including the coastline, this is probably the biggest problem faced by photographers such as myself. This is a shame since the NT looks after a large chunk of our heritage and they are preventing the recording of heritage buildings and land, so this is being lost to future generations. As I work in black and white film I feel closer to the historical record than maybe I would if I was using digital. They will counter this by saying that they commission a lot of photography but that misses the point; no-one takes a photograph like I would so they have lost my interpretation and recording of their properties. You can of course continue to take commercial photographs from public rights of way across National Trust land.