H&C and Circle trains to and from Hammersmith use the original "Bishops Road" platforms alongside the main line station, from which the rest of the station can be reached by the walkway you mention. District and Circle trains to and from High St Kensington use the "Praed Street" platforms which are connected to the main concourse (known as the "Lawn", because the GWR always had to be different). The Bakerloo platforms are more-or-less underneath the Bishops Road platforms but have barrier-free interchange with the Praed Street station.