Arrived in LHR on Monday at 1645 from NCL.
Got on the Picadilly, seat for myself and seat for my bag.
Had to give up the seat for the bag at Acton Town (IIRC) and then changed at South Ken for the Circle....whole trip hassle free.
Incidentally, made it back to Clapham at 1815.....quicker than last time on the HeX.