London Buses operates a bus from Peckham to Canary Wharf every 5 minutes. Tickets cost $3 and the journey takes 6 min. Alternatively, London Overground operates a train from Peckham to Canary Wharf every 20 minutes. Tickets cost $1 - $3 and the journey takes 6 min.
From Bermondsey, Galleywall Road South Bermondsey Stn line 1 bus to Surrey Quays Station. 6 min £2. From Peckham Rye train to Surrey Quays. 6 min £1. From Peckham taxi to Canary Wharf. 13 min £22. From Peckham Uber to Canary Wharf. 13 min £11. From Peckham walk to Canary Wharf. 1 h 14 min. From Rodney Road , Walworth Bikeshare to Fisherman's Walk West, Canary Wharf. 33 min.