According to our local planners, of whom I do have experiences with ....just because you already have something, it does not follow that you can alter than something without permission. Just thinking, if its a tight turn as you say, why has the previous owner not widened the gateway ....is it because they were not bothered about it, or they had tried and been refused permission?
Our planners do not like the natural stone wall being altered, or pulled down, and would probably say no. There is also the problem of who owns the "extra" land you will be driving over, once you take the wall down? Is it yours or the public highway? Daft as it may sound, and I have been through this when trying to alter an access point, there is the issue of highway safety. They can argue a bigger gateway means larger vehicles reversing in and out etc.
Obviously, your planners may be fine, and say its a good idea. First off, I would ring the planning department up, and ask if you require planning for what you want to do. Sometimes they will come and visit the site, and tell you there and then, if its ok. If you have to put in for planning for removing the wall and widening the entry point, they will charge a fee, so I would just ask first, and try and save the money!!
If you don't ask and go ahead, then the council find out and say its wrong, they will make you reinstate the wall to how it was. So in my view, its best to ask and see how the land lies.
Good luck with it!