If you want deaths registered in 2013 (note the registered there. Somone could die in 2012 but have a death registered in 2013) you want this page: http://www.ons.gov.uk/ons/rel/subnational-health4/suicides-i... which links to a spreadsheet with the data.
They use a clear definition of what they count as suicide.
If you want to know suicide rates in different regions you want the (unfortunately named) NUTS3 document: http://www.ons.gov.uk/ons/about-ons/business-transparency/fr...
If you want deaths registered in 2013 (note the registered there. Somone could die in 2012 but have a death registered in 2013) you want this page: http://www.ons.gov.uk/ons/rel/subnational-health4/suicides-i... which links to a spreadsheet with the data.
They use a clear definition of what they count as suicide.