Been there, done that, got the T-shirt and the hernia. (Very glad the kids are a little bit older now.) If you give us a bit more information about the journey you're actually trying to accomplish, we might be able to find better alternatives.

For instance, are you just passing through London on the way to somewhere else? Are you staying in London at all? What are your destinations/origin points for Liverpool Street and St Pancras? (I'm guessing you're coming into Liverpool Street from Stansted Airport or Harwich cruise terminal, and going on from St Pancras to Paris -- but that's just a guess)

FYI, I have had (limited) success pushing one luggage cart and pulling another -- but it's definitely a pain in the rear to do.