My mother is 82 and is the same, her legs are weak and she always feels wobbly, unstable and does fall at times.
She was in hospital for a month, for a problem resulting from Aortic Valve Stenosis and seems her physical strength has worsened since she left. We spoke to the hospital's social workers, who arranged a care package for her, so she has carers come in the morning to get her up, washed and dress, then another comes at lunchtime, to prepare her meal and finally another to help her get ready for bed.
Care packages are means tested and an assessment was done, to ascertain her suitability for care, which she passed. A financial assessment was also carried out. The client, will usually only be asked to contribute to costs (�16.50) per hour, if they have savings of over �18K, but obviously the less personal savings, the less the contribution will be.
My mother was in hospital for 4 weeks and has been out for 3, she's been feeling a bit down, as she hasn't really been out for about 7 weeks, so I've invested in a wheelchair, so we can take her out on trips.
The best thing to do, would be to contact social services. if you contact your relative's GP surgery, they will have the phone number for the relevant department. The rules with my mother's local authority was a telephone assessment initially, if that's passed, they advised someone would visit within 28 days, but obviously, this can be too long, so I would definitely talk to her GP to hurry things along. If she's still in hospital, then you would probably get faster results.