Have you ever tried taking suitcases on the Piccadilly line? As another
poster has said, HEX and taxi is the way to go.

Yes, frequently. They even took out seats on the Picc to allow for
more luggage. HEx and Taxi is the way to go if you're

i) rich
ii) on expenses

and iii) staying at a hotel in Paddington

I've encountered a lot of hostility to normal underground services,
mainly from the USA, who think it is a den of Bronx style iniquity.