Just a note about travel in the UK. From London to Edinburgh by train takes between 4.5 to 5 hours so the best part of a day is taken by travel each way. Even if you fly check in times and travel to and from airports can take just as long. Driving that distance is just not worth it ..... I would concentrate on one country and see what you can in the time you have available.

Being Scottish by birth and having travelled a lot around I would opt for Scotland as it is much smaller and a lot more can be seen within your timescale. The only drawback is the midgies when you get into the countryside in July.

What ever you chose I hope you will enjoy the trip.