This thread has some info.
https://polishforums.com/uk-ireland/nearly-impossible-passport-appointment-london-86175/#msg1771702This explains the documents you will need, how to arrange an appointment, how to collect the passport and what to do if you don't have all the documents they want: gov.pl/web/wielkabrytania/paszport-dla-osoby-doroslej
This is where you apply online:
secure.e-konsulat.gov.pl/Wizyty/Paszportowe/RejestracjaTerminuWizytyPaszportowej.aspx?guid=0e9b2958ac5d489da805cbc76a925f01