The best scenic routes are to the east, since to the west it is a bit restrictive between LHR and Gatwick airspace.
Kent in general is quite nice, if you stay away from Maidstone, that is... you cannot go wrong with a general bimble well south of the Motorway there.
Nice places to go to in a 1 hour flight:
- e.g., souteasterly Bewl Water - Leeds Castle
- e.g., east to the River Medway, follow it to the isle of Sheppey [caution, Rochester ATZ], then down to Leeds Castle again
For a longer flight, the absolute best is to go east via Canterbury [nice by day, stunning at night!] to north of Dover, descend to 600ft off the coast [not at night...] and fly along the cliffs [well below clifftop!], climb back inland over Folkestone [but make sure your climb rate is up to it] and return via Ashford [not pretty, but a very interesting looking mall...]