The 52 bus will get you there.
About 3 miles.
The nearest tube station to the Victoria and Albert Museum is South Kensington which is on the Piccadilly, Circle and District line. Once you leave the station the Museum is about a five minute walk away.
Kensington - Olympia - station was created in 1844.
South Kensington tube station was created in 1868.
South Kensington railway station was created in 1891.
West Kensington tube station was created in 1874.
High Street Kensington tube station was created in 1868.
The Science Museum and the Natural History Museum are both in Exhibition Road in Kensington, London. Nearest tube station is South Kensington. The Geological Museum and the Victoria & Albert Museum are also in the same road.
All depends which station in Kensington - go from Harlow Town to Liverpool Street on the train, then take the Circle Line (in either direction although eastbound's probably a bit quicker) to South Kensington station.
Queen Victoria was born in Kensington Palace, London.
South Kensington Station
Queensway