If you want to register your .london domain, just follow the process bellow:
The london priority Period is running until 31st of july 2014.
London priority Period, gives priority to registered trademark holders and Londoners applying for domain names.
Allocation of names during the first phase will depend on a priority ranking. The following is the priority ranking of customers:
Those in the Trademark Clearinghouse
Those having a London address AND a right to a name (e.g. it matches their business name)
Those having a London address for any name
Those without a presence in London
Where there is more than one application for a name those applicants will be validated by an external validation agent. If, after validation, multiple applicants for the same domain name end up in the highest priority ranking then an auction process will be used to determine who will get the domain name.
From 9 September 2014, Dot London domain names will be available on a first come, first served basis, During the General Availability