I took only a carry on bag for the 15 nights of our vacation. It is a Tom Bihn Tri-Star bag which has straps for wearing it as a backpack or to carry by hand or over the shoulder. You can find it here: www.tombihn.com/page/001/PROD/500/TB0940.
I mention this because having only one bag which I could wear on my back greatly increased the ease of travelling around London, and to and from London.
I was glad to have it as we stomped up and down stairs in the London tube stations. Have you ever been down the spiral staircase at the Tottenham Court Road station to get to the Central Line? It felt like the fire drill in my office tower. No chance you could drag wheeled luggage down those steps! And I was equally glad not to be dragging a bag over cobbled streets and to be able to store my bag above my head or under my seat when travelling on trains to and from Gatwick Airport or on our five day excursion to Bath.
I have to confessed, however, that my bag included a rolled up duffle bag which I used to pack souvenirs and gifts for my daughters back home. The duffle went as checked baggage for the flight home. We used Exclusive Airports car transfer service to get us to Heathrow since not only did I have an extra bag but my husband’s bag was heavy with bottles of single malt inside.