No, you are correct you won't (usually), find 737's cruising at 4000. However as your own diagram illustrates, there are lots of different parts of CAS all with different levels.
Although 737's don't usually stooge around at 4000, they do have to climb through that level to get to the cruise.
Many of the light aircraft want to cruise at FL80, 90, or 100. This puts them in direct conflict with passenger aircraft wishing to climb/descend through these levels.
Using your diagram again, you can see how many small airfields there are in the area... the performance characteristics of a lot of aircraft operating from these airfields means that they will get in the way as they slowly plod their way up to FL80 or 90, whilst doing 120Kts ground speed
Your route from Shoreham to Cambridge would not get to fly that way at any level in the TMA, because of the various holds for major airports, or various zones, being used by airline operators that pay for the service
If you really are talking about aircraft being allowed to fly VFR at 4000, then you really need to understand how the airspace is designed and why. The base is designed on climb characteristics of passenger aircraft leaving major licensed airports. It is there to afford some safety in the climb/descent i.e. the airspace base raised the further from an airport you get. That is why VFR is not allowed in willy nilly.
You really need to understand the reasons behind airspace design and not just throw your toys out the cot because you can't fly wherever you want. It is an intense area of aircraft operation. The airspace is designed to provide protection. Whilst not maybe the most efficient use, it is also designed to allow as much Class G as possible, e.g. underneath.
Unless you are willing to dig deep and pay quite hefty charges to facilitate extra controllers and support staff and equipment, I'm afraid the Utopia you are after willl not happen... even then with extra controllers etc, entry will be subject to traffic, you would not get charged if you couldn't enter.
In the ideal world, everyone would be able to do what they want when they wanted, but it is not the ideal world. The airspace, and ATC is funded by fee paying users, and it is in the interests of UK PLC to protect trade and get money into the country via passenger transport etc.