Several ways to do your first leg, the one you suggest seems OK (though I'd avoid Elstree zone to the north - perhaps BNN instead) From Compton, I'd route DCT Alderney unless D026 was active, in which case a slight dogleg via Swanage.
On flying into the CI's expect to be asked for an eta for crossing zone boundary (50N if approaching from the North, 2W if approaching from the East)