A VAT registration number

Yes - NIP = VAT

... as it says on Wikipedia.

You could have looked that up for yourself!

Yes I think so

It looks like the NIP number is allocated when you set up business in Poland. It is their tax identification number and is also used for vat purposes.

HMRC (bless 'em)

list Poland VAT as 'PTU' or 'VAT'.  However in a lot of European countries they have a tax ID number which is also used for VAT.  If it starts 'PL' it probably is their VAT number.

ED:- See also http://ec.europa.eu/taxation_customs/vies/