Have name-changed for this.
I don't consider us rich, but many people would (net worth £x,000,000) because we don't live a lavish life-style, more like a very middle class one (5 bed semi in London, private schools, 4x4). We don't struggle financially, but we certainly aren't tossing money around (buy most things discounted and spend carefully carefully). We have no debt and spend our money wisely - no business class tickets or lavish holidays for us. Sure, we could live a more champagne lifestyle, but then we wouldn't be able to invest for our future and the future education of our children.
DH comes from a working-class European background, but worked hard in school and managed to get a full scholarship to an American University. He did well there, got a job in finance, got a masters from an Ivy League business school, and went into banking.
I grew up upper-middle class, but was given no handouts beyond having my education (undergraduate and graduate) paid for.
My parents are even more wealthy than we are (net worth $xx,000,000), but they definitely don't, and never have, viewed themselves as rich as the bulk of their net worth is tied-up in investments. My father emigrated to the US with a graduate degree and worked extremely hard. My mother also worked until her third child came along. There were no foreign holidays for us and every space cent was re-invested, resulting in them having the net worth they do, and a retirement annual income the same as when my father was working.
I think that education, working hard, investing well, and spending frugally have been the reason we have been able to acquire our net worths.