If you are working then you'd put your little one in Nursery / Day Care same sort of set up as in NZ, waiting lists for the good ones / not all days available etc seem to be the challenges I've heard from friends.
If you are SAHM / work PT / have nanny then from 3yrs til they start school (the September of the year they turn 5, so feasibly when they have only just turned 4 but can be deferred until the January) there is Pre School / Nursery School (very much like Kindergarten but they dont use that word here), which is usually just mornings for 3yr olds and sometimes longer days as they get closer to going to school. Good Pre Schools have HUGE waiting lists, my local one is full up for the year Hayden turns 3... he is turning 2 in a few weeks, we've gone on the waiting list and while they were able to accomodate most of the waiting list this year that is no guarantee. A local friend got a guaranteed place by registering her son when he was 12weeks old!!!! Put you name down at as many as you can so you have a chance of getting something.
info on pre school / nursery school
Once they turn 3 children are eligible for 15 (or is it 20 hours??) for free, if its an option at your school you can pay for them to attend more sessions. Sometimes you can pay for them to attend from 2.5yrs. Hmmm eligibility for the free hours might depend on your visa tho - do you have 'recourse to public funds'? To give you an idea of costs our local Pre School charges £8.50 a session which as I said is mornings only pretty much but I suspect other facilities might have different hours / sessions available.
Look up the website of your local council, find the pages on Education where you'll put in your postcode and that will tell you the options in your area. The OFSTED report is what will tell you if its a good facility or not (1 = excellent, 2 = good, wouldnt bother with less than that TBH).
You should be able to find a local Play Group, ours runs twice a week £1.50 a session (9.30am to 11.30am), parents stay and supervise child in what is essentially organised free play. Its a pretty good way to meet local parents, everyone helps with the chores to make everything run smoothly and its a 'come and go as you please' thing so no waiting lists etc
Hope that is helpful, we are in Reading which unfortunately is a fair way from Portsmouth otherwise we could of had play dates!!!