Late Payment from Big International Company

Hi there. I am new on here but need some help.
I own and run a small Science Education business and work with some big organisations that are known globally. I had trouble last year with this particular organisation and it took them 63 days to settle my 14 day invoice, following numerous phone calls, emails etc. etc. I suppose I should have learned my lesson but I went ahead and worked for them again this year in August and I am still awaiting settlement of my invoice. I have emailed, left messages and am getting nowhere. What should I do?
Trouble is you are unable to contact their finance department from outside and so all dealings have been with the head of the Education Department (the individual who booked me)
On Monday I sent them a final warning stating that I would withdraw all services to them from now on unless they paid immediately. I have heard nothing and have run out of patience. It is also seriously affecting my cashflow.
Advice please...

Thank you for your quick response! You are certainly correct with the comment re bureaucracy! You just cannot speak to anyone who has authority at all..

I suppose that this is a good learning curve for me and I shall not fall foul of this again. The majority of my customers are good payers and pay on time.

I have contacted the errant company again this afternoon and am awaiting a call back. If none is forthcoming, I will certainly ramp it up as suggested.

Thanks!