That won't solve anything. Let's say that you leave London and 10:00 UTC, and land in another city at 15:00 UTC. Do you go to dinner? Breakfast? Can you schedule the business meeting at 17:30 UTC or this is just after midnight?
I worked in UTC for almost 3 years because it was company policy to have just one timezone for operations. Granted I was in Europe so the impact was minimal on my life, but not having DST and always working in UTC saved a great deal of problems when dealing with clients around the world on a real-time basis. The only organisation I ever had a problem with was the BBC because some of their people would regularly struggle to know which way was up.
Just get an extra clock and keep it in UTC.