Don't even think of it without GPS and radar cover.
Radar cover is almost an irrevelance - you will see little traffic about on this route on a genuinely IMC day and in any event the chance of hitting someone is way less than the risk of an engine failure. Of course it just might happen. For that reason I personally prefer to use some form of TAS or to be in receipt of a service but many quite reasonably dont. In reality you will get a service most of the way. Farnborough North and West will take you just about from west of Heathrow all the way down to the edge of the downs - thereafter you might persuade Solent to give you a service if you ask nicely, but dont count on it because it is outside their remitt. You could route through Luton and SVFR through Heathrow if the base is high enough.
GPS is nto a bad idea if you doubt your ability to navigate. The airspace along this route is quite tight in terms of avoiding the various bits of class D and class A. You will not be kindly received if you infringe. On the other hand with radar cover you will get some warning although obviously that is not something on which to rely.
If you are itending to stop at Bembridge assuming it is open and then return to Elestree the cloud base will obviously be very relevant because neither have an useful let down. It is relatively safe to make a cloud break at Bembridge from the east (over the sea). If push comes to shove you can probably negotiate a let down at Southampton or for sure at Shoreham if for example it is a matter of getting visual below a base of 800 feet or above. Neither are good locations for a made up let down at or in the vicinity of the overhead with high ground and masts around. Nor are you likely to get an accurate indication of the base. I would leave that for those folk who "know" what they are doing.
If you go anywhere near Parham do take account that they often have gliders up with surprisingly low bases.
one can pick up airways intersections
I think he means most GPS setups will have the airways intersections in their database effectively like another set of VRPs although hopefully more certain that they have been accurately included! Obviously with a GPS you can use these for a steer and the controllers will be familiar with them so if push comes to shove you can either ask them for a heading or indicate that a particular intersection is your next RP.