If you find that after school care is necessary and there are no after school clubs available, you could use a childminder. These are like babysitters but they would collect your children from school and care for them in their home, and they are licensed and approved by the local council.
Alternatively you could advertise for someone to collect your children and look after them in your home. A nanny who currently has only a morning job might be available.
This is what a few of the parents around here do. Some have also hired students from the local University that are studying to become teachers.
As far as obtaining a place in primary school it can be very tricky as others have mentioned, especially if you are applying mid year. IIRC the class size for key stage one (years 1&2) are capped at 30. There is no guarantee that you will receive a place in the school closest to you.
Also keep in mind that you can't apply for a school place unless you either have a tenancy agreement (if renting) or have exchanged contracts (if purchasing).
Once you have narrowed down where you would like to live you can always go to the local education authority site to find out about admission policies. Ofsted is good for seeing how well the school did at their last inspection.