You can get contactless PAYG prices without any identification in London by using an Oyster card. You can buy them from corner shops without ID, and top them up at the same places with cash.
I doubt this really affords you any extra anonymity though. Tube and rail stations are so heavily covered by CCTV, and the police have many times tracked peoples entire commutes and movement through CCTV only.
To hinder traffic analysis across multiple trips, you should also have meeting where you swap Oystercards with others, similar to how people would (and still do?) swap grocery purchase tracker cards with each other, to get the discount with less surveillance.
I doubt this really affords you any extra anonymity though. Tube and rail stations are so heavily covered by CCTV, and the police have many times tracked peoples entire commutes and movement through CCTV only.