byrnedjp how weird, I just posted about this on another thread and attended my first 'Work Based Interview' the other week....
And I used to work in the job centre.
I presume you are on Carer's Allowance and are claiming Income Support as a 'top up', just like me.
You need to contact the Jobcentre asap and explain your situation if you really can't attend the interview at all or need to postpone, otherwise you stand to lose benefits if you don't keep them informed.
Basically if you write down how your day is made up of caring and outline your duties as a carer and the traits of your uncle's condition which demand you are on call 24/7 (as I expect is the case) that is as much as you can do. Email them with this info and explain that you desperately WANT to work but your situation dictates that, for the foreseeable future, this is impossible. It would be a very good idea to add what you are doing to keep your 'employability' up to date, ie accessing online computer courses to update your skills. Google things that might help you, document what you have done (dates, sites visited, results etc). If you haven't been able to find something suitable then ask them for ideas and links to skills that you can access online for free (food hygiene courses for example) and if they can't come up with anything that fits the bill that's their failure to help you - you tried.
They cannot demand that you leave your uncle unattended to make this interview if that jeopardises his safety (be sure to use that terminology) so don't be bullied. You can insist they rearrange for a time that suits YOU if you are a carer (I checked this on the phone when I arranged my own interview). Please do message me if you need more help. It is too easy to be intimidated by these appointments when in fact they are SUPPOSED to HELP you.