My strong advice is to go to Richer sounds and buy these and save £21 from your budget.
https://www.richersounds.com/hi-fi/h....html?brand=76
https://www.whathifi.com/q-acoustics/2020i/review
One of my kids bought a pair when he started Uni, he is a music nut, they perform very well and he has been very happy with them for the last couple of years.
Words of warning:
Your other kit is on loan, so if your mate wants it back you can easily sell the speakers to a local student.
Your records may not be in very good condition and you may find the experiment fails immediately.
Think very carefully if you want to get into this hobby. It can get expensive, especially with records.
If you want music in your home, you could sell your records, get a nice little digital system and make a big profit. Your collection may be quite valuable and there are thousands of sharks out there who will lie through their teeth to get their hands on collectibles for a fraction of their value. So be very careful. You get best value on eBay.
My younger son's audio system cost £129 + a spotify subscription, comprising Alessis active speakers (£99) and a Chromecast (£30).
If you really are determined to get into audio, and it is a declining hobby because kids aren't interested (they use headphones from a phone) and digital audio has knocked the stuffing out of it, you can get a perfectly good turntable from Richer for about £200, a Yamaha integrated amplifier with a phono input and digital inputs (so you can stream from your phone or computer) for about £300, and possibly a cartridge upgrade for about £50.
A lot of people here trade second hand units, lots of it vintage. Speakers do wear out. Vintage kit can be unreliable. You do not need that grief. Some people advertise at the "correct" price, a lot is overpriced as it a buyer's market. I once bought vintage (my elder son's home system) from a very reputable shop (Audio Gold) with a 6 month guarantee, and Quad because it can still be factory-serviced at fixed prices. I would stick to Richer: Yamaha, Onkyo etc. great value, just as good, and you get a 12 month guarantee.
Wilson, Luxman, Innuos, Holo May, Puritan, Garrard