And that will nearly always have an impact, and I have no doubt that, in the US or the UK, wealth affects the lawyers you can afford and that affects the justice you can get.
Justice may be blind, but she sure recognises the smell of money.
The only ways I can think of to preclude that are either for the legal aid system to buy the best lawyers available (and we can't afford it), or for legal representation (good or bad, cheap or high-priced) to be assigned at random by the state, and I expect that to happen about half an hour past forever.
Money talks. Always has, always will. Unless we abolish money, and all substitutes.