I don't see it being a problem as long as you have a passport that allows it. I was flying from JFK-FCO-BCN a few years ago and missed my connection in Rome. The next flight to Barcelona was like 6 or 7 hours away. I had to exit anyway, through customs, to rebook. Rather than going in I roamed around a bit at the limo for hire area. I found a company that charged me the cost of a round-trip to a central Rome hotel plus some reasonable amount of Euros per hour to give me a tour. Great English speaking driver. I had never been to Rome before and it was wonderful.

London should not be a problem, I have gone through there with a US passport for a 4 hour stay before. I explained to the immigration officer that it was a mileage run and he said, "I don't want to hold you up any longer for your very short visit to our country" gave a chuckle and sent me on my way.