In order to make it clear that any payment is a reimbursement and not a wage all expenses that are paid out should be on the production of a receipt and for auditing purposes should be signed for by the volunteer. You may want to produce a form that volunteers can take home and get their carers to fill out as a receipt as many people will choose to pay someone who is not a professional and may not automatically give receipts. When deciding how often to reimburse expenses and whether to pay by cheque or cash do bear in mind that care costs are likely to be quite high. In order to make it viable for people on low incomes you should probably think about reimbursing as promptly as possible in cash.
As long as you are reimbursing expenses and not paying the carer directly the legal relationship is between the volunteer and the carer they are paying. Whether they choose to use a professional registered carer or would rather pay a friend or relative is entirely up to them. If something goes wrong and the carer is at fault you do not have any kind of duty of care so can not be sued. Equally you have no responsibility to ensure that the carer is declaring their earnings and paying tax and National Insurance. However it may be a good idea to make sure that the volunteer understands that it is the carers responsibility to do this and that if they choose not to they could potentially get into trouble. You may want to draw up a childcare policy outlining this and reiterating that as an organisation you have no responsibility for the relationship between carer and volunteer. If a volunteer is having problems finding a carer it is not a particularly good idea to suggest people as this may indicate that you have checked the carer out and know them to be good. If you put them in touch with your local Childcare Information Services they will be able to tell them about care options in your local area.
The Department for Education and Employment has established a childcare information helpline and website called ChildCareLink which puts people in touch with their local Childcare Information Services who will hold details of local childminders, playgroups and nurseries:
0800 096 02 96
http://www.childcarelink.gov.uk
The Daycare Trust is a national childcare charity.
http://www.daycaretrust.org.uk
There are not such comprehensive sources of information about paying for care for adults but the following sites contain some useful information:
http://www.carersonline.org.uk
http://www.carersinformation.org.uk