Is there a mid-career trap for professional engineers in the UK?

My question concerns technical career paths for mid-career engineers (not SWE) in the UK (i.e. US-centric advice might not apply here).

Current situation

I'm a design engineer with ~10 years of experience, working for a branch of a fairly large company (not London nor Oxbridge); my position is modelling/physics/design heavy and more niche compared to perhaps more widespread SWE/MechE/EE etc. I joined this company 8 years ago, working to Staff/Lead level. I have been lead engineer on several projects and the outcome has generally been good. At year-end reviews I exceed most of my goals, I volunteer for stretch assignments, I mentor interns and graduates, the works. Plus, I have almost 10 patents with this company and a couple conference papers in my name.

Basically, I do everything I can think of and I've read about to further my career. Education wise I've got a MSc, but I haven't observed an appreciable difference in trajectory from the PhD-qualified engineers in my department .

Issue

My salary is low and my growth opportunities look pretty stifled. Between salary, bonus and RSUs I gross about £65k a year. I have tried to push for a substantial adjustment and promotion this year but the response was no, mostly owing to no openings for existing positions. A move to engineering manager is also not an option. I know of several colleagues in my position that left, but in a different engineering field in which more companies are hiring.

Looking elsewhere, the outlook is not great either: between recruiters calling me and my own searches (including through my own small network) I can find maybe 4-5 matching positions at my level (Principal or above) in the whole of the UK; the ones I've applied to, usually result in interviews and about half in offers, but:

• The comp and org chart level is practically on par with what I make now
• When it's substantially more, it's pre-seed startups with a vague product proposition and what I consider high-risk, low-reward business plans

Just for fun, I went on a few interviews for jobs in the continent (mostly Netherlands/France/Germany) and the comp difference in the offers I've been receiving is astounding (+100% for some offers from Big Tech/FAANGs). I have a family and I have been trying to do anything I can to avoid uprooting them, but I'm becoming despondent of the possibility of keeping building a viable career in the UK.

Question(s)

1. Is the lack of internal and external opportunities for career growth compared to what's available to say, PMs and Business Line managers, a common occurrence in the UK? There seems to be no growth opportunity in a technical leader path that don't involve basically becoming a business guy or a pure manager.
2. Am I missing some crucial execution step to unlock career growth?

Depends on the company.

For example, my ex-employer (IBM) explicitly has career growth paths for technical employees, though to reach the highest levels you need to explicitly start building specific kinds of skills and credentials from the start of your career, making yourself someone upper management will pick out as a technical advisor and innovator. And in the upper levels you do start doing less direct tech and more team lead/architectural work.band the top technical levels still don't get paid as well as the top managerial levels.

In other companies, it may be presumed that everyone will move into management of some kind, though if managing a technical team you may still have the opportunity to stay involved in the actual development. If that's your situation, you need to decide how hard you want/need to work to carve out a niche you'll be happy with.

Talk to your management. Explain what you're looking for. Ask them what career growth paths are available for you, and exactly what they need to see from you to justify that next step. Then plan accordingly.