I am sorry to hear this situation - it is frustrating when these situations can occur especially so late on in the recruitment process.
The first thing to mention is that the firm won't need to rescind as such, it will be more than the terms of the offer cannot be met. I just want to make this clear as I don't want people to panic that other offers could easily be rescinded.
Are you graduating this year or will your course be carrying on into the next academic year? I ask as if you are graduating from the course this summer it may be possible to move to this internship visa if the firm is happy to cover the costs of this:
https://www.lawsociety.org.uk/topics/firm-accreditations/tier-5-gae-scheme. However, you will need to consider your general visa status as a student, as I am fairly sure you can only have one visa valid at one time, and therefore it maybe too complicated to move from a student visa to this visa and then back again.