What is the procedure?
you need to fill out the necessary forms (available online from the Polish consulate in the US) and send them along with a fee, some passport photos of yourself, and your birth certificate (original), then just wait a few months for your passport to come in the mail.
In theory you are supposed to report your income to the IRS but once you start working abroad using the id of a foregin country (ie Poland) you are more or less "off radar," besides unless you are making serious cash I doubt the IRS would be interested in you
by the way your PESEL may come in handy so once you have a passport you will need a personal id card (dowód osobisty), but to get that you will need a permanent address in Poland. this is more or less how it works in chronological order:
1. Get your Polish passport
2. Go to Poland and get a relative to allow you to register as a resident at their place of residence (they will have to help you with the forms, sighn papers, etc)
3. Use this info to fill out a request for PESEL number
4. use the PESEL number to get a personal id (more paperwork)
Then once step 4 is completed, you should register OUT of your relatives place and go to England...technically you can be in England while most of this is taking place, you will have to periodically go back to sign forms, pick up ids, etc.
Good luck, this takes patience and the whole process should take about 6 months give or take a few months..