It depends on your cared for and your own needs for respite and on the resources of your borough.
But yes, in theory one day a week at a day centre isn't really much to ask for. My OH went five days a week for years, so why stop at one?
Contact your council's Adult Social Services team and ask for a needs assessment for him, and a carers assessment for yourself. You're entitled to one my law. Only once the need is established should they do a financial assessment, which will determine how much the cared for would have to contribute towards the costs, if at all (lunch is an extra cost). Your own money will not be counted.