How crucial is university prestige for Oxbridge postgrad applications?

Hey everyone!

I was wondering, if a person has a good profile for Oxbridge but came from a low ranking university, what are the chances that they will get accepted?

Here's my background:
I have achieved a first-class grade (85%) in Computer Science and served as the president of my university's main tech society, organizing hackathons and events. Additionally, I've published a research paper in the field of AI/ML. It's worth noting that my university is one of the low ranked unis for Computer Science; in fact, it's considered an arts-focused institution being one of the best in that field. I am also an international student completing my bachelor's degree in the UK. Given these factors, what do you think my chances are?

Thank you very much for your insights.