You can't go directly from Euston to Gloucester Road. You would have to take the Northern Line south to Leicester Square (3 stops) and then the Piccadilly Line west to Gloucester Road ( 6 stops).
Various AM stations carry weather, but in the US, the National Weather Service (NOAA) channels are above the FM band, around 162 Mhz. There are special settings on some FM radios that can pick up...