You need to discuss this with your solicitor/conveyancer.
The Land Registry official register plan will determine what you own. The plans you have put up here are, I think, probably just the developer's plans. They may, or may not, be the same as the transfer/TR1 plan on which the Land Registry official register plan is based. However, it is not unknown for the plot plans given to prospective purchasers to differ from the transfer plan as things develop on the ground, and developers don't always update them as they should. If there is a discrepancy your conveyancer should have picked it up, assuming he/she knew about the original plan. However, the first thing is to establish what exactly you own. What you think you see "on the ground" is not always consistent with the legal ownership.
Secondly, even if the strip falls within your ownership, there may be a planning condition or other matter that affects it and which effectively takes precedence. Again, your solicitor should have told you about this.
Speak to your solicitor/conveyancer and check the actual position. You need to know your legal position and the actual facts. I think it most probable that the developer is correct in what they are saying (you could, of course, check this out with the local authority - although that might risk enforcement action). It is possible that you could have some action against the developer if they misrepresented what you were getting or your conveyancer if they have been negligent or, most likely, it could just be a misunderstanding. In any case, you need to establish the facts first.
I think it was probably precipitous to take the "internal" fence down given what you had been told about the existence of a wild life corridor. Personally, I think it sounds rather nice, and a good thing. But in any case, if it is a condition of planning, you risk enforcement action, so I would be careful about checking the facts and your legal position before creating too many waves.