OK, so in the UK, "nursery" can mean both "private day care" and "state funded preschool".
For private daycare, there is often a very long waiting list, and I believe that prices in London can be of the order of £100/day! These settings are open 50+ weeks a year, usually only closing for a few days at Christmas and bank holidays, and usually open 7.30am-6pm, I'm speaking from my non-London experience; in London open hours may be longer. These settings are the more flexible option for working parents.
For state funded preschools, they are open term time only (39 weeks a year), during school hours, and open to children from the term after their 3rd birthday. So if your child's birthday is 1 Sept, they would be eligible for a place IF THERE IS CAPACITY the following January. At this age, all children are entitled to 30 hours a week. Many settings will dictate when/how this can be taken eg: in 5 blocks of 3 hours from 9 am - 12 noon, or 1-4pm. Going to a preschool nursery attached to an infant/primary school, does not guarantee a place at the infant/primary school.
There are many tunes to play on the state model, and the preschools may not be as "free" as one might first imagine.
Children in private daycare nurseries are also entitled to 30 hours at 3+, and again, private nurseries often have conditions on how this can be used.
Those are the two basic types of childcare "nurseries". There are variations, and every one allocates the way the 30 hours can be be used differently. In London you are probably going to be looking at long waiting lists.
There are also childminders and nannies.