If the flight is at 1030, you do not need to be there for 0730. Many airlines may not even have opened their check-in desks by then. (BA, for example, opens check-in for flights between two and three hours before departure.) Furthermore, as previously mentioned, most airlines will charge excess baggage on a 25kg-suitcase, primarily due to 'elf 'n' safety rules stating bags over 23kg must only be handled by two people. Finally, conformance was mentioned above but at this point in time it only applies to BA and Virgin, neither of which operate from T4 where the OP appears to be going. (It is rolling out to other airlines at Heathrow next year.)
As a regular traveller between Southeastern-land and Heathrow, my suggestion for that route is Catford to Victoria, District to Barons Court or Hammersmith, and pick up the Piccadilly there. Next best is Catford Bridge to Charing Cross and walk down to Embankment for the District.
I do not encourage going from Catford Bridge either to London Bridge or Waterloo East for the Jubilee then changing at Green Park (horrendously long walkway) or going to Charing Cross and joining the Bakerloo line (also long walkway and the change to the Piccadilly at Piccadilly Circus isn't great either). The route changing at London Bridge and Green Park is, however, step-free.
As a regular traveller between Southeastern-land and Heathrow, my suggestion for that route is Catford to Victoria, District to Barons Court or Hammersmith, and pick up the Piccadilly there. Next best is Catford Bridge to Charing Cross and walk down to Embankment for the District.
I do not encourage going from Catford Bridge either to London Bridge or Waterloo East for the Jubilee then changing at Green Park (horrendously long walkway) or going to Charing Cross and joining the Bakerloo line (also long walkway and the change to the Piccadilly at Piccadilly Circus isn't great either). The route changing at London Bridge and Green Park is, however, step-free.
District goes past there too.
