Well, I did find flying round London a bit scary the first time. Many years ago now, but I was glad to have another PPL next to me.

Ideally I'd make the first trip in good clear weather so eyeball navigation is easier (even if you've got a GPS, also a good idea). Get a service from Farnborough, and they'll generally warn you before you bust CAS vertically or laterally (and make sure you squawk Mode C). Midweek (rather than a weekend) means less traffic to see and avoid, and you get more attention from the (excellent) Farnborough controllers.

You can't fly much inside the M25 because of controlled airspace or built-up areas (as you can't go above 2,500 feet, so glide-clear doesn't take you very far). On the West there's Heathrow. Yes, it's now Class D, but there's a good chance you won't get let in, so you need to have a good plan B and be ready to use it. Round the edges there are several tight gaps such as by Farnborough in the SW, Gatwick/Biggin in the SE, White Waltham/Wycombe in the NW and near Stapleford in the NE.

There are few places in the UK where a PPL has to keep such accurate vertical and lateral navigation for an extended period.

Nothing desparate, but a bit challenging the first time. And great fun.

And in a single, even if you are let in, you certainly can't go in to much of it due to glide clear requirements!

Having done a lot of flying out of Fairoaks I can vouch for the problems with the "Mig Alley" bottleneck between Gatwick and Heathrow / Biggin, particularly difficult in the evening, flying West into the setting sun - best avoided if possible. I suppose the same is true flying East in the morning, but I never got up early enough to try that!

It used to be straightforward to get a SVFR clearance when routing North from Fairoaks through the LHR zone, routing Thorpe, Ascot, Burnham not above 1000' - and similarly southbound. I've not flown there since the change to Class D, so I've no idea if getting clearance for that route is easier or harder to get now.

FBW

There shouldn't be an issue transitting most London airspace depending on how busy they are at the time! When the London CTR was class A, I was granted special VFR as a student on a nav. ex. no worries! was over foresst mainly and not above 800ft mind!

Had your navex authorising instructor taken leave of his senses? As if Heathrow ATC wants students on navexes transitting the London CTR…
Utter madness.

Why should flying round the London area be a "black art"?

So long as you do you homework and seek advice like you are doing here and from pilots/instructors who have experience of doing these sorts of flights there is no issue.

I would hope that if your PPL training had been conducted properly you would feel competent to conduct almost any cross country in good VFR conditions.

Like Chilli Monster has previously said if you need any help I am also around Tollerton and would be glad to assist.

PPL Virgin, have a look at these;
https://www.youtube.com/watch?v=n65oQhQx9K8
https://www.youtube.com/watch?v=AVC9JTc5_p0

Its pretty easy :ok:

These are good -

VFR Airspace Guide | Airspace & Safety Initiative

They were released by NATS a while back on DVD (you may still be able to get them) and has Irv Lee conducting several flights around London to show you the things to look out for.

And see Take a guided tour of UK skies | NATS Blog for an idea of how much is wizzing around just above you! I love the bit showing near-horizontal views of the stacks around London.