Should I get new glasses?

Can't comment on if you need new ones however, for cheaper glasses check out glasses direct! I used them personally and it was so smooth and seamless (Plus much cheaper than highstreet!) 🙂

I recently had an eye test, and my prescription has increased; the opticians called it a "significant increase", whereas, in my opinion, it is only a slight increase. My original prescription was -1 in both eyes, and now my left eye is -1.50, and my right eye is -1.75 with -0.25 astigmatism.

I am unsure if I should get new glasses as I am only a uni student and glasses (as well as the eye test) seem to be so expensive and I'm just not sure whether it is worth it with such a slight increase.

I have a super complicated one and have had no issues at all, they have a good refund policy but they are made by an optician 🙂 You can also order a few frames for a free home trial to try them on before ordering. I am super fussy and did this 3 times before finding the ones I wanted 🙂

You're substituting your opinion for the opinion of a trained professional. Why would they say this was a "significant increase" if, in fact, it was not?
Have a look at the NHS Low Income Scheme if you haven't already -- see https://www.nhsbsa.nhs.uk/nhs-low-income-scheme
Included in the scheme are "the cost of sight tests, glasses and contact lenses".
Be aware that the page states that "You should get your certificate within 4 weeks of applying" -- so it would be best to apply as soon as possible.

What is super complicated?

Sorry worded poorly, my prescription is complicated but I had no issues at all and they offer chats with a optician if you need it 🙂

Thank you for that; I have considered it but have been unsure whether the frames would be fitted ok and whether the prescription would meet my needs due to not being fitted by an optician. What has been your experience?

If you fill in the prescription correctly there should be no problem with the fitting of the lenses... frames are more difficult to fit. I'm an optometrist and I was ordering online when I was a student, had some misses with the frames, some where uncomfortable others where just not sitting well on the face, but the majority of the glasses I bought online where perfect. The quality may be lower than the optician ones, but for their price they are totally worth it.
I've never ordered my progressive ones online or with any special coatings, but the regular sunglasses or anti-glare ones I ordered a lot.
As for if you need a new ones because of the prescription change, it depends on your visual acuity with the old ones. Although the change in the diopter may seem significant, the change in the visual acuity may be small and if you can manage without straining your eyes with the old ones, there is no real need for a new one.