You are quite correct that this new procedure will be implemented from 1st July 2011. The EU-South Korea Free Trade Agreement (FTA) is a bilateral agreement, so qualifying goods will incur a reduced customs rate at import, just as your export items would currently for qualifying countries under the EUR1 scheme.
However, this new FTA is not the same as other preference agreements (i.e. the EUR1), and you must register to become a part of the scheme.
The agreement between the EU member states and South Korea will operate under a Registered Exporter Scheme, and to become a registered exporter in the UK you must apply to HMRC using form C1454 (visit www.hmrc.gov.uk and type C1454 in the search box for the latest form). If your application is successful then you will be given an Approved Exporter Registration Number, and you should then quote this on the export invoice with a statement that you verify the goods qualify for preference.
If you already use the Registered Exporter Scheme for other countries, then you should contact the issuing office of approval (probably HMRC in Leeds) and ask for it to be extended to South Korea.