Why don't we just go to the scottish highlands?
Lake district is nice but it's pleb teir in comparison to the scottish highlands.
We fly to glasgow airport, from glasgow you can get a train or bus to pretty much anywhere in the western highlands. Train from glasgow to Crianlarich (about 2 hours on the train) and then we climb Ben More, and camp on the summit.
Or we could train to fortwilliam and then climb Ben Nevis, highest peak in the UK, both are pretty easy.
https://www.youtube.com/watch?v=qPk5XEApEa0 