Thameslink operates a train from Covent Garden to East Dulwich every 30 minutes. Tickets cost $5 - $7 and the journey takes 12 min. Alternatively, London Buses operates a bus from Covent Garden to East Dulwich every 10 minutes. Tickets cost $3 and the journey takes 36 min.
From London Blackfriars train to Peckham Rye. 12 min £4. From London Charing Cross train to London Bridge then train to East Dulwich. 28 min £6. From Temple, Lancaster Place Somerset House line 176 bus to East Dulwich, Goose Green. 36 min £2. From Covent Garden taxi to East Dulwich. 14 min £25. From Covent Garden Uber to East Dulwich. 14 min £19. From Covent Garden walk to East Dulwich. 1 h 32 min.