If I were coming from the West....
I would be speaking to Farborough Radar and request MATZ penetration, overhead transition, and route Overhead Farnborough -> Guildford -> OCK -> EGTF making sure that Farnborough knew which route I was intending to take.
The problem with the danger areas is that they may be active and if you are a newbie it's just more stress you don't really need if you want to go over \ through them and you can't. If you ask for MATZ penetration, over head transition and route Farnborugh -> Guildford -> OCK then if Farnborough can't provide it then they'll offer something else (quite possibly through inactive danger areas) but will usually provide QDM to Fairoaks for you.
Also remain south of the bagshot mast because it's heathrow north of that.
That's just what I would do, other mileage may vary and it's not the most direct way but I think it's one of the easiest way to do it.
I would overfly Farnborough by 2,000ft and if they needed me higher then I'd do that. I don't have my charts with me but I think 2,500ft is the london TMA above it, which is all class A and I wouldn't want to be that close to since my altitude holding is not IMC precise and it would be easy to stray into it.
All very imho of course.