I doubt anyone will find a hoist in the kitchen suitable.
The hoist needs to be so placed that it can be used to tranfer your husband from his bed which if carers are involved will have to be a hospital bed to the shower and toilet.
No-one would contemplate either a commode or bed-pans being used in a kitchen!
Ideally, your husband needs a bedroom with adjacent shower, hand-basin and toilet in a room that has a wide enough door for a wheel-chair to be used, if and when one becomes applicable, His bathroom must also be large enough for whoever helps him to shower to do so without getting soaked themselves. The toilet seat will probably need to be raised and hand-holds drilled into place in the walls on either side of the toilet and shower.
Not living in the UK, I do not know if you can get any financial help for all these facilities.
You cannot care for your husband without carers coming in - n o-one can and do not let social services palm you off with suggesting that your adult children or other relatives help.
No-one who is not a trained nurse or carer should risk trying to move a handicapped and possible heavy person - you can hurt both your husband and yourself seriously unless you know exactly what you are doing.
And you really will be even more in Queer street than you are now if you damage your back or rupture yourself trying to move your husband.
I realise this sounds harsh, but the reality is harsh.
I am sincerely sorry you are in this horrible position, but as your house is not suitable for an invalid, you probably will find that carers neither can nor will be sent in.
Please do not feel guilty. You are not forcing your husband into a nursing home and you did not cause his accident. It happened, and as the hospital does not think rehab is an option and have apparently not felt physiotherapy was applicable either, I am very much afraid you have no choice here and that a care home is the only option right now.
What kind of prognosis are his doctors talking about? Is his mobility likely to increase? Will rehab or more physiotherapy become applicable soon, or not?
Have you insisted on a second opinion? It might be well, for your own peace of mind to do so.
If your husband is not able to comprehend the seriousness of his situation, or even the reality of it, then you and your children will have to assume the responsibility for making a very tough decision.
I hope you can find a doctor or other medical professional person who can and will help you decide what is best for your husband, which is obviously your first priority, and what is necessary for you to be able to continue living a reasonable life in harsh circumstances, You really must consider yourself as well as him.
If the cost of a permanent care home is too high, and there is no possiblity of your husband being able to return home, now or later, you may need to consider selling your home and finding a small flat for yourself if by doing so you can better cope with the care home fees. Not something you want to do, I know, but it might be well to consider it, while looking at your options.