If you are planning to carry out any works to your flat you may need some or more of the following permissions. They are important. If you don't get the right permissions, you will have a problem selling your flat - quite apart from risking enforcement action from the Corporation if they find out.
It can be a criminal offence to carry out work requiring listed building consent without authority, so consult a surveyor or check with the Corporation before going ahead.
Under the terms of your lease, you have to get written permission from the Barbican Estate Office, before carrying out any alterations which affect the structure (including any fixings to walls) or any alterations to the kitchen and bathroom. You should send them a description of the proposed works and a “before and after” sketch plan or drawing. You'll need a 'licence' approving the works before you start; and a letter after the works are completed approving the way they were done.
You may also need Building Regulations Approval from Building Control at the Corporation. Their role is to check that work is carried out properly. If Building Regulations Approval is required, you must get a letter from them when the works have been completed, confirming they comply with building regulations.
If when you come to sell, it turns out that you don't have the necessary consents - e.g. you didn't get consent when you took out your Garchey or when you laid wood flooring - then you will have to get 'retrospective consent' or else undo the works. Don't take it for granted. You may be in trouble if you have done work requiring listed building consent without permission. If you have done work which the Corporation as landlord wouldn't have approved at the time, they won't approve it later. In fact, you could be worse off - if their attitude has changed, then they may refuse retrospective permission later for work they might have approved at the time. If your work involves altering or installing pipework or connecting into (or capping off) communal conduits, they make you open up the wall to prove the work was done right.
The Barbican have rules on doing alterations - the hours when your builders can drill - and "tips" - so your carpet installer doesn't put a nail through the under-floor heating.