She'd be in reception in September, if they were looking for a setting right away when they move it'd be nursery year.
Yeah the terminology can be confusing can't it? School Nursery, Playgroup, Day Nursery, or Preschool all will offer provision for three year olds under the same curriculum called the Early Years Foundation Stage (which also covers Reception year). It's all based on learning through play so not really "schooling" per se. Not as formalized, if you see what I mean. If you have any questions on that,feel free to PM me.
Getting together with other mums is called things like Mums & Tots groups or baby group or toddler group. The Netmums website will list any in the area.