Waterloo station - about 10 minutes walk.
If you mean the Royal Hospital, Chelsea - which isn't a hospital, it's almshouses for retired army personnel - the nearest main line station is Victoria and the nearest underground station is Sloane Square.
Sydenham railway station - London - was created in 1839.
Rainham railway station - London - was created in 1854.
Central railway station - London - was created in 1880.
Central railway station - London - ended in 1940.
Woodside - London - railway station ended in 1997.
Woodside - London - railway station was created in 1871.
London Fields railway station was created in 1872.
London Road - Brighton - railway station was created in 1877.
London King's Cross railway station was created in 1852.
Braunston London Road railway station ended in 1958.
Braunston London Road railway station was created in 1895.