Mark wrote:
What's the best/quickest/safest route to get from Liverpool Street to
Hatton Cross on the tube on a Sunday morning about at 11.

Mark

If carrying luggage etc, Circle Line to any District Line station on the
south side of the Circle, e.g. Embankment, St James's Park or Sloane Square.
Stay on the same platform and wait for a District Line train to Baron's
Court or Hammersmith, (showing either Richmond or Ealing Broadway as the
train's destination) then a cross platform interchange directly onto a
Piccadilly. No stairs or escalators, except at Liverpool St and Heathrow.

You can go on the Central Line to Holborn and change onto the Picc there,
but it is a long walk between the two with an escalator to descend if carry
luggage.