My next thought was to get a bank account to proove address, however they wont let you open one without a NI number and again proof of address.
Some banks have special arrangements for people from other EU countries (especially Poland) who need to open an account but don't have an address. I think Barclays and the Co-op both do it.
She can also go on the Electoral Roll without proof of address (maybe at yours?) and they will send acknowledgement.
Also anyone can apply for an NI number without proof of address, and again, the letter and card would be sent to whatever address she applies from.