Have you not read the rest of this topic in full, or more importantly, the consultation documents from the Nominet regarding this? I'll assume you haven't, as the documents and the posts on the previous pages answer this question you posed:
No, as per the documentation, as it currently stands (Nominet haven't fully decided yet), they will first offer .uk domain names to TM holders, once all the good domains have been mopped up by them, it will then go to those with registered and unregistered rights, such as current owners of the .co.uk, .org.uk, .me.uk versions of .UK domain names, and the .UK will go to the highest bidder.
That's if they don't decide to automatically grandfather .UK's to owners of the .co.uk's, .org.uk's or .me.uk's, then it would go to those with no rights who would all have to go to auction for anything that's left, something like that anyway, I may have left a stage out.
The consultation document is here;
http://www.nominet.org.uk/sites/default/files/Nominet_FINAL_electronic_form3_0.pdf (See page 13, section titled "K. Phased release and rights management")