Some leases have a further line which says that consent cannot be unreasonably delayed.
At the moment, the neighbour can say that she is not denying consent and reasonably, she just hasn’t made her mind up!
The matter of the balcony is not relevant. It doesn’t matter whether she has the balcony or doesn’t have the balcony although there may be issues over maintenance of it in the lease which would need to be overcome.
Ignoring the point I made about her saying that she is just delaying giving consent rather than denying it, you go ahead regardless, she will have to take you to court to get the work stopped pending approval and whilst that might seem to bring the thing to ahead, she may not bother with that but when you come to sell, in landlords replies to any enquiries, she may say that you never had consent and you are in breach of covenant in the lease so whilst it might seem to be a solution, it can be problematical further down the line.
If she simply resolutely decides that she isn’t going to consent but at the same time, not refuse, but just ignore you, bearing in mind that she is one half of the freehold, then there is no legal mechanism other than taking her to court and you hoping that the judge does not raise the issue of consent being delayed rather than denied.
A solicitors letter requesting the consent officially (rather than threatening court) may have more notice taken of it initially if there is a formal offer in the letter to do the terrace.
You wouldn’t have any claim for any financial implications (Other than legal costs of course)regardless.
Can I clarify anything for you?
Please rate the service positive. It’s an important part of the process by which experts get paid.
We can still exchange emails. Best wishes.