Disclaimer: I don't fly in the UK so what works here might not work there.
For both of your scenarios I would file IFR (in flight for scenario #1) and give them some waypoints as a general indication of my flight path. I'd then tell them I'd be operating "upto 10 nm either side of track" or whatever you wanted to make it, and request clearance or traffic information as appropriate.
Specifically for your London scenario, I'd give a central waypoint in the area I intended to be operating, give a radius of operation and altitude, and request clearance based on that. Also, it would be a good idea to call the relevant ATC, on the phone before flight, and just tell them what you want to do and ask them how they'd like you to do it.