I am moving from the UK to Dubai. Please would you explain which documents I need to get attested and where / when / who / how do I get this done?

You need to get your university degree attested along with Marriage Certificate and children’s Birth Certificates if you are bringing any family to live with you in Dubai.  These are attested at the Foreign Office in London followed by the UAE Embassy in London.  Finally the process is finished at the Ministry of Foreign Affairs in the UAE.  Please see these links from Move One Relocation who will be able to aid you in the process.