I'd echo the previous post. I've flown across the Atlantic literally dozens of times. Even on the larger classes of aircraft now coming into service, the bathrooms are too small for two people to have much room to maneuver. Changing a baby diaper in an airplane restroom must be very difficult; changing an adult just isn't feasible.
If you can change before you board the plane, and have something like an ABU Space - which is, in my experience, the highest-capacity disposable available - you might just make it through the flight. Once you land, there should be family restrooms (much more plentiful in Europe and the UK than in the States) where you can change before you go through immigration.
The key, as BambinoBaby mentioned, is saying no to the beverages offered during the flight. I'm sure you'll be a little dehydrated, but managing that is going to be much easier than managing a wet diaper in flight.