Are the houses in a conservation zone?
Even if they're not, I think there is a good chance that you won't be allowed to alter the second house to remove/replace the door. Of course it very much depends on the nature of the houses - I'm assuming typical mid-late Victorian / Edwardian terrace.
Do you need planning permission to interconnect the two houses? You can own the two houses and live in both of them without any planning permission. I can't see any reason why knocking through between two terraced houses would ordinarily require planning permission if all the changes are internal. However, you should get advice from an expert - which I am definitely not.
One piece of advice is to think hard before integrating the two houses. It may be better to keep separate electricity, heating, etc. in case you want to sell them again as separate houses. I suspect that in most cases the price you'd get for selling them separately would be more than selling them as a single property - not least because of the stamp duty. See this story about Jamie Oliver:
http://www.standard.co.uk/news/celebrit ... 23761.html