It depends where you are in the country as it's a bit of of a postcode lottery, but theoretically there are day centres, sitters/befrienders, carers and respite in a care home. You will have to ask for this and be a nuisance to get it. Call up Adult Social Services and ask for a needs assessment for the caree and a carers assessment for yourself. You're entitled to one by law. Tell them they have "duty of care for a vulnerable adult at risk" and that you are close to carers breakdown.
Also, call your local Carers Centre, Alzheimer's Society and/or Age UK. They can signpost services and give emotional and practical support. Look for things like lunch clubs, Singing for the Brain etc. They can help fill in forms like Attendance Allowance and Carers Allowance if eligible, council tax exemption, power of attorney etc. and they can act as advocates if Social Services give you the run around.
Good luck!