I previously worked for the predecessor of McGinley, the 'Storm' predecessor, indeed I became in charge of flight crew recruitment for Storm and as you mention 'Italy' I have a feeling I know of the 'BPA' airline, as a rule of thumb all Italian airlines are slow payers and I have personal experience of BPA's beancounters late paying and needing to be, frequently, shouted at.
As I recall the agency work on about a 15% margin of the individual's salary, i.e. if the contractor is getting 10k per month then the airline is paying the agency 11.5k of which the agency take 1.5k.
Please read your contract thoroughly, I don't recall it ever being written in to a contract that the airline needs to pay before you get paid, moreso it was contracted that you shall be paid on X day of the month with no mention of the airline needing to cough up the dosh first, you work for the agency, should the airline not pay then that is the agency's problem, not yours.
But, invariably, it doesn't work like that, working on a 15% margin the agency needs to be paid for seven months to support you by just one month and should they pay you before they have been paid themselves that is a sure fire way to go bankrupt.
If you are an England & Wales national then 'Money Claim Online' might assist, it is the County Court of England & Wales, often referred to as the Small Claims Court, I'm currently suing eBay thru it, OK it's not an employment tribunal but then McG don't employ you as an employee do they, they owe you a debt so I would recommend investigating if Money Claim Online might be of assistance to you.