to try to give you a little more pleasant advice... (geez, louise)
the thing i always find brings a prompt response is to remind people of the late payment of commercial debts (interest) act 1998, as amended 2002. in fact, i always now put reference to this on my invoices, but if you haven't done that it this instance, it's not too late.
basically the act gives you a right to levy a fine for late payment (after 30 days, unless otherwise specified) and to start changing interest on the unpaid fee.
details of the act are here:http://www.berr.gov.uk/files/file37581.pdf
basically, you have the right to charge £40 for late payment if the amount owing is under £1000 (£70-90 if it's more), and to start charging the bank of interest base rate +8% interest.
in your situation, i would write one final time to the big-name company concerned, politely spelling out when you first invoiced, for how much and then saying something along the lines of ' I would like to draw your attention to my statutory rights under the Late Payment of Commercial Debts (Interest) Act 1998-2002. Under this, I am entitled to ... blah, blah. I'm afraid that if I have not received payment for my original invoice in 7 days [or 14 days, if you're feeling generous], I'm afraid I will have to send you a bill for the fine amount and start changing interest.' blah, blah.
As this is the one thing guaranteed to get accounts people in trouble with their bosses - their actually costing the company money - they usually always react promptly. I guess it's not foolproof, but I can say that it's never failed me yet, and it's a lot cheaper than being forced to pursue legal action.
In future, it might be helpful to append to your invoices something along the lines of
Payment terms: 30 days, please
Please note my statutory rights under the Late Payment of Commercial Debts (Interest) Act 1998-2002 to charge a fine for payment after the due date and to levy interest (8% on top of the Bank of England base rate) for any amounts outstanding.
That won't stop the numerous b*stards who always pay late, but it does put you in a better position from the start.