Some childminders will do home pick up and drop off, but that tends to be the exception rather than the norm.
Contrary to one of the earlier comments, childminders do not usually charge for a full day while a school aged child is in school. Some, by no means all, will charge in the case of a child being in nursery especially if the childminder remains 'on call' to pick them up in an emergency during nursery hours. Childminders normally charge by the hour or have a flat rate for school runs.
IIUC you’re seeking a door-to-door service between home, school and back again. Many childcare providers will shun that because it doesn’t allow time to build up a relationship with the children involved, while simultaneously disrupting the way they care for other children. It can also result in the unwanted side effect of every parent wanting home pick up/drop off, or accusing the childminder of favouritism.
The far greater problem is that some local authorities consider what you’re asking for is a taxi service, rather than childcare. Some local authorities require childcare providers who offer that 'taxi service' to register as licensed cabs, which is prohibitively expensive.
As mentioned, that leaves you with either a nanny or babysitter. Be aware that some, but not all nannies are Ofsted registered, and Ofsted do not have any sort of dealings with babysitters. You need to use a registered provider in order to make use of any financial help such as childcare vouchers, Tax Free Childcare, or the childcare element of tax credits.
Be very cautious with unregistered childcare, as you’re essentially allowing a stranger lone access to your children with no background checks. They may also be invalidating their motor insurance by taking money to drive children to school, unless they have a proper commercial or specialist childcarer's policy; IOW they would be uninsured in the event of an accident.
Be aware that you will remain entirely responsible for your children if you place them with a non-registered person because they cannot legally be responsible for someone else’s children. That means that if, god forbid, they are harmed or involved in an accident, you may get a call from social services.
This all means you need to make a lot of thorough checks, references, and demand to see documentation above and beyond what parents normally need when seeking childcare.