I usually post on the Private Aviation part of the forum....but as I know quite a bit about EASA having dealt with it for nearly 7 years now, here goes. BTW I do not work for the CAA but represent a section of the aviation industry on regulatory matters!
One needs to understand that the scope of EASA's functions are 'limited' (!) to the following, very briefly:
1. Drafting pan-EU implementing rules for original and continuing airworthiness (incl. maintenance), licensing, operations, training establishments etc etc for approval by the Brussels based administrative and political system
2. Certification of aircraft on a pan-EU basis (for which they charge industry)
3. Oversight (through 'standardisation programmes) and audit of member states' implementation of the rules
Whilst this is a large programme it does not cover what member states still have to do as part of a (so-called) integrated EU approach. Thus UK CAA still has many functions at member state level, covering what EASA does not cover. Much of the certification functions of the UK CAA have disappeared in the last few years. So progressively the UK CAA does not draft or set the rules within the government political framework, but it still has to implement someone else's (the EU / EASA) rules.
As to funding, I learnt many years ago when working at a senior level for a UK government agency, that the difference between this side of the pond and the part to the west of us was that west of us, once the taxpayer had paid for something it was then made available to the public for free. Whereas this side of the pond once the taxpayer has paid his taxes the job of government is to find every opportunity for charging the consumer / public to pay (again) for the service. A big philosophical difference. The UK CAA does not get a look in on the first part of that - tax payers' money.
Maybe it has something to do with ambitious and some would say unnecessary flagship programmes of free-spending governments over here.
But there we are.