Hi OP, not posting this to hoist or be smug - posting so you (and others) can see it IS possible for the private sector not to treat you like a mug.
I work for a huge global private company. I'm pretty much bottom of the food chain. Been here for over 20 years, but I love the company and I especially love my current role (so much so that I've done this rule for over half of my time here). Our pay scales are benchmarked nationally and then scales at 80-120%. If you sit below 100%, in theory you get a bigger pay increase annually compared to those over 100% (subject to getting at least a meets expectations).
A few years ago, I had my annual pay discussion and went away to mull it over. I realised that I had been in the role for 7 years at that point, and when I looked at my percentage of scale, I realised I had gobs down from 94% to 93%. I looked back over previous years and realised I was basically hovering around the 94% mark. So I mentioned to my boss that I was a bit disheartened as it was essentially a pay cut in a way because if I'd stayed at the same % of the scale when they reassessed the scales, I'd have actually been on a higher new salary than what I had been given annually. Anyway, I thought I was just having a bit of a grumble and that would be it. A month or so later she called me to tell me that she had been impressed with the way I had gone about arguing my case (genuinely did not think that was what I was doing but hey ho) and so she had gone to the GM to discuss it. He completely agreed and said basically they wanted to recognise my experience in the role and the crucialness of that to the business and were giving me an out of cycle pay rise to put me up to 100% of the pay band! I couldn't believe it - I had never had a pay increase of that size.
The following year, or maybe even the year after, I got an exceeds expectations (so not as good as OP's Outstanding) - I got an 11.9% pay rise. My manager (different one to the previous one) told me that he appreciated everything I did and would always give me the largest possible pay rise he could from his pot. I'm not on just shy of 104% of range - so it's grown by several percentage points despite it supposedly being harder to do that post 100% compared to those 7 years at the 94% mark).
The point is, even multi billion dollar corporate machines can recognise even the tiniest of cogs on their business and look after them. Having a decent manager to back you helps. But not being afraid to express your dissatisfaction and disappointment is also important. State facts. Argue your case. If they truly value you, they'll want to keep you - and a few extra thousand a year is nothing to them, but everything to you.
For context, I was on around £25k before all this. I'm now on £34k for the exact same role just 5 years later (with next pay review due shortly). I have another new LM and he has told me that previous LM had shared with him his he looked after me and has promised to do the same. I admit I've been extremely lucky with my last 3 managers and so that's played a big part in this!
Good luck OP. Work out what you want, what you think you're worth, and go for it!