South Western Railway operates a train from Brixton to Twickenham every 30 minutes. Tickets cost $6 - $11 and the journey takes 19 min. Alternatively, London Buses operates a bus from Brixton to Twickenham hourly. Tickets cost $3 and the journey takes 37 min.
From Vauxhall train to Twickenham. 19 min £6. From Sloane Square bus to Twickenham, York Street Twickenham. 37 min £2. From Brixton, Shakespeare Road line 345 bus to Clapham Junction then train to Twickenham. 56 min £7. From Brixton taxi to Twickenham. 23 min £48. From Brixton drive to Twickenham. 23 min £2. From Brixton Uber to Twickenham. 23 min £22.