My last house had a similar covenant along the lines of 'you may not build anything without our permission' but the council estates department always treated it like a formality and readily gave permission every time we made an extension. Understandably it may vary from authority to authority.
I'd give these other neighbours a knock to ask a) did they actually ask permission b) WHO did they ask in the council c) how long did it take?
I'd give these other neighbours a knock to ask a) did they actually ask permission b) WHO did they ask in the council c) how long did it take?