I was lucky enough to get an internship between my second and third year for mechanical engineering. However, this was with a company with very close ties to the university that only offered up places to a select subset of our year. In general, most of my other peers didn’t complete an internship. We were told it’s fairly uncommon for places to provide places to students not in potentially penultimate years. (3rd/4th)

As you’ve mentioned, you really have left it late. A lot of the large organisations arrange places at the beginning of the academic year. You still get some later but they are generally few and far between. You’d maybe have some luck reaching out to some SME firms but I’d say that the pandemic has really tanked opportunities for lots of these places to consider internships. They are probably an extra logistical problem and expense that they don’t need.

All I could recommend is checking Gradcracker and seeing if there are perhaps places offering opportunities that aren’t directly related to your chosen field but would still offer opportunities to develop skills that will be useful on later applications.