Not in a university in England on the UK tax payer's dime.
For research, and for taking UK students. NOT for taking overseas students.
Universities are private institutions that get paid by the state to do specific things. A few do opt out of this.
At least that's how it works in the Netherlands where I've looked into it, and that's with subdidies available for EU students who often don't stay here and don't contribute to taxes later. Source, in Dutch but the graphic near the top is a good summary, where the lower bars are "costs" (kosten) and the higher bars "benefits" (baten): https://www.cpb.nl/de-economische-effecten-van-international...