Not as nice as Kingston because Kingston is much newer. But from HI Brentford, you could take bus 267 a short ride will take you through Kew Bridge Rail station 30 minutes to Waterloo or 20 minutes to Vauxhall. This bus will continue pass by Gunnersbury (immediately outside the station) and later Chiswick Park (short walk, 3 minutes), Stamford Bridge (4 minutes walk) and terminate in Hammersmith tube station.

Also some other bus will take you to Boston Manner or Northfield in 15 minutes time. Or Ealing Broadway if you take the bus longer, possible 20 minutes time.

Bus 237 will take you the same route as 267 but take a turn to pass front door of Stamford Bridge, Goldhawk Road, Shepherds Bush and then White City.

The nearest rail station is Brentford but requires a 10-12 minutes walk or a simple bus ride. Connect to Vauxhall and Waterloo.