Beware the forum rule that the number of opinions expressed is equal to the square of the number of people participating in the discussion.
Seconded! And let me add: all recommendations you get on the www are worth as much as you paid for them.
Questions to ponder:
-) where to land to clear customs?
-) how much flying over water are you comfortable with?
-) recommended/mandatory equipment for flying over (a lot of) water? wetsuits, raft, ELT, ...
-) how to make sure of either sufficiently good weather for the full duration of the trip OR sufficient spare time to wait for said good weather?
-) flying "VFR on top" might increase your options regarding weather but comes with its own issues
All of these have been discussed over and over, I suggest you search the www a bit and come back with more detailed questions.
PS more pointed answers could be given if you indicated the type of plane and more or less where you would start from - Kent doesn't make for the same routing as Scotland.
[[edited to add: apologies, I had overlooked the _London_to_ bit of the heading ]]
[[and Baikonour below has it right: time enough to look into the details ]]