(Hey, I'm just sharing some opinions in the interest of discussing usability... hope this doesn't come across as negative.)
I respect what this initiative is doing (prioritizing actual accessibility and equitable access to government services, see [1] and [2]), but IMO they go a bit far in serving the "lowest common denominator" experience to everyone.
Yes, the website is simple and clean, but IMO in doing so, it sacrifices information architecture/ease of navigation (especially for browsing), and has a generally poor visual hierarchy.
There's no easy way to skim the "Services and information" section short of reading all 16 entries, which all look the same and are arranged alphabetically. And that section looks pretty much the same as "Popular" and "Featured", and is followed by "Government activity" and "More on Gov.uk".
It's dozens of links to manually comb through, in a long vertical scroll, before I can figure out where to go next. My eye loses its place easily in these long, undifferentiated lists. I can't compare links above and below the several folds (vertical screen-spaces worth of scrolls). The search isn't great either, and returns a similarly long lists of undifferentiated links with low relevance and no autocomplete or manually curated highlights for popular queries.
The takeaway for me (again, just IMO!) is that it's totally fine to use either "progressive enhancement" or "graceful degradation" to ensure all users can use your site, but you shouldn't stop at the most "accessible" version. Accessible !== plaintext! Companies and researchers have spent many decades and dollars exploring and improving best practices over time that help sighted users with color vision navigate in many ways that can be better than "long lists of text". Those users shouldn't have their experiences limited by what screen readers can parse any more than screen reader users should be limited by graphic design. It's totally possible to do both, and give different audiences each a great experience.
I use gov.uk "heavily" and what I find interesting is that I never go to their homepage and try to navigate myself to where I need to go. I either receive the email with a link to a page or I google the pages I need. Never had issues finding anything.
I think this is important because it's not a standard e-commerce page, so it's not about skimming content and trying to sell/engage users as quickly as possible.
It's also not a SaaS like page that focuses on a few use cases and nails them. Gov.uk probably provides 100s (if not 1000s) of different flows, for everything from managing your driver's license to incorporating a company. Organising and navigating a large tree is harder than search imo.
But yes I agree, it could be improved it just wouldn't make a difference to me.
For React, I prefer the astoundingly good MUI framework (amazing components with lots of customizability, a good enough default look, and great documentation): https://mui.com/ If you end up going this route, using their Figma kit (https://mui.com/store/items/figma-react/) plus the Refactoring UI book from above should allow you to whip up a pretty standard-looking, "pretty enough" design in very little time. And then implementing it using the actual MUI lib would just take a few days.
You should know the basics of accessibility (beyond general usability, this alos means alt text, header levels, contrast ratios, readability, screen readers, keyboard navigation, special considerations for the hard of sight and hearing, etc.): https://www.w3.org/WAI/standards-guidelines/wcag/ or at least use an easy checklist tool like Microsoft's WCAG analyzer: https://accessibilityinsights.io/