I graduated with an MEng in ChemE and after 7 months of industry experience, I've entered my 2nd job and now I make £35k/yr + benefits + bonus
I would say that the one thing nobody tells young A-Level students when they choose a degree is how if you study engineering, it is a high probability that you will have to relocate to non-desirable places in order to make these big salaries. For example, senior safety case engineers at Sellafield make a lot of money, but they probably had to relocate to the edge of a country to begin their careers (I had to move quite far from uni myself), and then have to relocate again to Whitehaven or somewhere else in Cumbria to be able to work on-site at Sellafield. So yes, you can make a lot of money, but it requires a lot of sacrifice.
In terms of making buckets of money by working in the finance industry, I honestly am not sure how it works or how easy it is to transition since it is something that never really interested me. Senior engineers in the nuclear industry make good enough money for me, and those kind of jobs are usually protected by a union as well, so you're basically set for life.
Luck plays only one role in a successful career. Skill also plays another part (and I don't mean how good you are at your degree, I mean more about how good you are at writing CVs, cover letters, attending interviews, etc.). But generally, as a rule of thumb, getting progression about your career is about being at the right place at the right time (if you stay at the same company). You can move elsewhere, hence changing the "right place" aspect of that equation, to accelerate your career, but you can only accelerate so much. At the end of day, years of industry experience dictate how much you get paid... and also your level of seniority/responsibility.