The whole issue here is the validity of the case being brought. Yes, people should have the same access to the courts regardless of wealth etc. However, there have been plenty of cases where unpleasant people (not necessarily with money) have used the courts to pursue and harass someone who has done no wrong. Normally, it ends up with the target taking a big financial hit as well. All sorts of spurious and malicious claims. Many of these have been done with public funds (legal aid) as well. I've personally known a lot of people who have had to defend themselves with their own money, whilst their spouse (or ex-spouse) has got legal aid and is relatively unaffected.
Sadly, access to courts can never be independent of money, because apart from anything else, it affects the quality of the representation you get. If you put a legal aid barrister against a £10k a day barrister, there's an immediate issue of quality. Obviously, if you've got an easy, solid case, you might be OK. But, anything that needs arguing etc., you could well be at a distinct disadvantage.
As with a lot of things, I feel radical change is necessary to make it as fair as possible, but whilst also removing the abusers. Can't say I know how to do it, but the system at the moment is generally not fit for purpose.