As a former international student, I just did a full body shudder in horror about your forgotten student visa paperwork! I'm glad you were easily able to sort it out — it's so easy to forget when it's a separate physical document.

My student visa when I was an MPhil student was printed inside my passport, but the year after that the UK transitioned to little physical plastic biometric cards (the same size as a bank/credit card), which is what I had for my PhD. You were meant to carry them in your wallet all the time, but I never did in case I lost it, which meant having to remember to add it to the wallet every time I travelled out of the UK. I only forgot it once, and, thankfully, this was on a trip to Ireland. The UK and Ireland have a common travel area which means that the UK treats people entering the country from Ireland as if they've just been travelling domestically within the UK, so there is no passport control and no document checks at the airport (although Ireland does make UK passengers go through passport control, and theoretically the UK authorities can come in and do random checks, but they never do). I spent the whole trip in an absolute panic that border guards would be there at the airport, and only relaxed once I finally got out of the airport.

I never forgot that student visa card again!