rustle
For starters, the TMA's are already full, as are the airways feeding them - hence slot times and height capping.
Are the airways and TMA's in the UK really full? According to
2001 movement figures, LHR is the 15th busiest TMA in the world. ORD, ATL, DFW, LAX, PHX, DTW, MSP, LAS, DEN, STL, MIA, IAH and PHL are all busier and allow PPL IFR traffic in as a matter of routine. Maybe the TMAs are not full, but the supporting infrastructure is slightly over-stretched.
As I said, there is a model out there which proves what is possible. It's attitude which prevents it happening.
Fuji
I for one would however prefer to be regulated by our good old national authority and not by the States (as much as I like Americans!)
Very nice, but a bit old fashioned

Like it or not, the UK has handed it's ultimate sovereignty to Brussels by treaty. So the relevant question now is whether you would rather be regulated by the EU or the US?
Well, as far as aviation matters goes, IMHO the UK would be better taking the FARs, photocopying them and renaming them the ANO, and then becoming an FAA region. Of course you would also have to persuade the UK government that tax on Avgas is to be ring fenced and used for the direct use of the person paying the tax, sort of how the US looks at it. That would require a governmental culture shift which will not happen.
In another thread ATC people are saying that BA pays for radar services so GA should shut up. You see it's all about attitude, GA needs the clout to point out that AvGas taxes are for the benefit of GA, and ATC should be lucky they have VFR traffic to control

A bit too much like the attitiude 'over there' I'm afraid.

But at least I have a high quality and safe IR which was cheap to get, cheap to maintain, and respected by even the superb controllers at the busiest TMAs in the world.