How will the COVID-19 pandemic affect graduate admissions? I have recently learned that all my internship offers were cancelled due to COVID-19, and I never felt this anxious before. People tell me I should not be worring since everyone is affected, but in my country research opportunites are very rare and nearly all of my previous experience is only vaguely related to my area of interest, in contrast to the offers I've  just been denied. This summer is also the most critical in my studies, since I'm more knowledgable than any time earlier and more likely to make an actual contribution.

I wouldn't be this worried if I could stay in the UK for my PhD (which is unlikely now due to Brexit), but I've almost finished my Fulbright application for graduate study in the USA. I would feel obliged to apply to US programmes if I were to be granted the award, but I'm not sure how I would compare with other students due to this gaping hole in my resume.

I guess what I want to know is if most students are in a similar position. Are other REUs and SURFs also getting cancelled or am I just unlucky? And most importantly, is there anything I can do to mitigate this and improve my chances for admission to graduate school?
I am not sure anyone here is going to be much help for your specific situation. There should be someone at your university you can talk with, a study counselor or someone similar. They can better gauge the current situation, especially at your own institute. And a bit more general advice: these types of situations can be very stressful, and I would advice to talk to someone about it. Just getting it out of your system can be very beneficial.