I used to be a union rep at one of the UK's universities. 

If you're a member of a union, see your union rep as soon as possible and take advice. 

From my experience as a university union rep, someone in your situation working as a university teacher would be able to get a few days compassionate paid leave, but no more than that - it would cost the university too much to offer more, given that someone else has to be paid to cover the classes you're no longer able to take. It might be possible to arrange a period of unpaid leave, which at least means the money no longer being paid to you can be used for temporary cover.  Perhaps a more practical option is that the timetable might be rearranged to give you some time off each week, or maybe your contract can be reduced on a permanent or temporary basis to give you one or two complete days free each week. 

I don't have any experience with school teaching, but I don't suppose your employers would be able to offer you any more than a typical university.  I'm sorry, because I expect this is most disappointing. 

As Telemando says, your rights as a carer may well be limited.
Before I retired I was a line manager in the NHS and this was not an infrequent situation. I would quietly point out to my staff that they were only entitled to 2 or 3 days compassionate leave. I would then ask them how receiving such bad news was affecting them and their ability to do their job and ask whether they'd considered talking to their GP about whether they should take some sickness absence until they were feeling less anxious and depressed? Most of them took the hint :-) 

Good luck
Dave

I’m a retired teacher and I know how difficult it can be to get time off even when you are ill yourself without it having a detrimental affect, Good advice to talk to your union rep. If you haven’t one at school your local union officer should be able to help. I’ve known people take the GP route as well. It’s worth a try if you have an approachable and understandiing GP. I guess it depends a lot on how supportive your headteacher is and the size and type of school you work in as to how flexible your timetable can be.

i hope you get this sorted out quickly. Don’t forget you can self assess for a week but a word of warning that could be a difficult route. Better to keep your doctor and school on board I’ve found.

Dont forget to look after yourself as well in this difficult time.

Sundial