Do you have states or provinces in the UK, and what are they called, how many are there?

Bit complicated this. We have two kingdoms - England and Scotland. We have one principality - Wales. We have one province - Northern Ireland. Apart from that we're divided (in England) into Counties or Metropolitan Boroughs or Unitary Authorities. Not sure what Wales, Scotland and N.I. are divided into since the last reorganisation.

In addition to Baloo's informative note.. yes Wales is also divided into counties though these have been renamed with Welsh names. Pembrokeshire became Dyfed for example. Scotland has its own government but it is not exactly a separate kingdom since the Queen of England is accepted there, indeed her consort, Prince Phillip, is named the Duke of Edinburgh for Scotland's capital, and the queen has residences there.
An excellent map can be found at the following ref. (adobe acrobat)
http://www.ons.gov.uk/ons/guide-method/geography/beginner-s-guide/administrative/england/counties--non-metropolitan-districts-and-unitary-authorities/map-of-the-uk-counties-and-unitary-administrations.pdf