I'm in the process of having my Polish citizenship done,
... only just now? What happened to the great patriot WP? :D (only teasing!)
It's a pretty straightforward process, but you need to be in PL unfortunately. What you do is fill out the form, and they confirm it via SMS. You put that code into the website, and it confirms your application. You then have to go to any Urzad Skarbowy or ZUS (and maybe some other places, but I'm not sure where) - and they verify your identity there. It's a quick process - my local tax office is walking distance, and the whole thing took me about 20 minutes, including walking to the tax office and back.
The only other way would be to get an electronic signature, but they're expensive and I think you have to be in PL to get one anyway. The EPUAP system is the "citizen-friendly" (yes, I know you won't believe that PO are making life easier...:P) version of electronic signatures.
Unfortunately, I think you'd probably have to go to the embassy/consulate to get the EPUAP verified - it looks like they can do it there - londyn.msz.gov.pl/pl/informacje_konsularne/informacje/
Aha, got it.
Osobiście udać się do jednego z wybranych urzędów:urzędu miasta/gminy, starostwa powiatowego, urzędu skarbowego, oddziału Zakładu Ubezpieczeń Społecznych, urzędu wojewódzkiego lub polskiego konsulatu by tam potwierdzić swoją tożsamość oraz zweryfikować dane osobowe z danymi wprowadzonymi do systemu
In short - you need to fill the form in, confirm it via sms, print out the document they give you (if they give you one, I don't remember), then go to the consulate/embassy with your passport and they'll verify it for you.