Given that a recent survey showed that tenants place a higher premium on having a balcony than even a car space, you certainly should claim a rent reduction for the period that the balcony is inaccessible.
Erring on the conservative side, you could calculate the proportion of the floor space that is no longer available to you and then ask for a commensurate reduction in rent.
Or you could estimate what you think the loss of amenity is worth, and claim on that basis.
Either way, the sooner you make a claim, the better; if you go to Tribunal, it will probably date any rent reduction from when the claim is made.
As a first step, go to the Tenants Union website and have a look at factsheets 04 and 06 which, although they don’t cover this specific circumstance, do offer guidance about how to make a claim.
Then write a polite letter or email to the landlord requesting a rent reduction for the period that the balcony is not available.