As has already been said, British Institutes is a franchise operation. Some are good and some are not. It is a little unfair - no, it's very unfair - to therefore simply refer to British Institutes and not say which branch you refer to .
BI are no different to most schools over here. Yes, some pay late, or find ways not to pay. Most offer contracts which are semi-legal at best, blatantly illegal in many cases. Some demand you have a Partita IVA (VAT Number) which means that you are declaring you are self-employed but actually work for a single school...which means you are actually breaking the law. The Italians are currently clamping down on such 'false' IVA's.
Look carefully at your contract. It'll almost certainly be a 'contratto progetto' which means a project contract. These are dished out like sweets because they relieve the school of the obligation to guarantee work, to provide sick or holiday pay and which are nonetheless illegal. A project contract, for example, cannot state that your project is 'teaching'.