Andy, I can't help with the planes and trains, but I wanted to check if you are aware of the new immigration rules into the U.K. for dual nationals? I only discovered them a few weeks ago and have had to cancel an upcoming trip to the U.K. in Easter because my children won't be able to comply.
Essentially if you are British or British by descent, dual national, (Which my children are) you have to travel on a British Passport to enter the U.K. British people are barred from applying for an ETA and the only way you can enter on a German passport, is by applying for a Certificate of Entitlement that will cost £589.
Sorry if you already know this, but I have a lot of Dual National colleague's , who like me, were completely unaware of all of this until a couple of weeks ago and it's caused a lot of upset.