As people have said, you don't have to sell the house. But consider carefully whether renting it is a good idea. I don't know what the market rent might be or the size of the house, but take a house with a rental of £600 a month, £7,200 a year. Furnished or unfurnished? If furnished, everything needs to be legally compliant, i.e. up to date fire-retardant materials, so it might cost a couple of thousand to comply with that (settee, bed, etc), and will need to be cleaned at every change of tenancy. The house will need to be decorated internally probably every year, and carpets cleaned, perhaps £500. All electrical appliances must be tested annually and properly serviced, so maybe another £200. Insurance of contents and buildings £500. Garden maintenance maybe £200. And the tenant will expect any faults to be rectified at once, e.g. central heating on the blink, faulty light switches, anything. Add on another £300 at least (a single plumbing emergency could cost that). Fees for the agent in finding a tenant and drawing up a contract, say £500. Fees for the agent in finding a tenant and drawing up a contract, say £500. Annual costs about £2,200 ignoring new furniture. Net profit £5,000. Less tax £4,000. That's just over £300 a month towards the care home fees. Will that make a difference to your mum? Oh, and bear in mind that with a short-term tenancy, there will probably be 2 months a year with no tenant, so deduct another £1,200 a year, making only £200 a month for mum's fees. And you might get the odd tenant who doesn't pay up at all.
Alternatively, sell the house for £150,000 and if all you need is £4,000 a year to pay the extra for mum's home, that will last you about 40 years.
I've painted a gloomy picture, maybe, but not unrealistic, and never mind the hassle of dealing with agents and tenants, gardeners, cleaners etc.
We sold mum's house, and spent £60,000 on a care fees plan that would guarantee a certain amount of income (about £750 a month) for life to pay part of her carehome fees. AS it happened, mum died within 18 months, so the plan was a "waste of money" some might say, but it gave me peace of mind.
Yes, SS will put a charge on the house if it can be agreed, and that might be a good way forward, but it will be snaffled by them when she passes away.
It is complex. If mum has the additional income from the rented property, it will affect her entitlement to pension credit too, so bear that in mind.
It's a minefield, isn't it?
Sorry, I haven't been of help, just put forward stumbling blocks, perhaps not what you wanted to hear.
Good Luck with your decision.
Margaret