According to recently published data from the London Datastore, for the first time in the 12 years recorded in their dataset, in 2013/14 Italy was the top country of origin for National Insurance Number (NINo) registrations to adult overseas nationals entering London.
In the 2013/14 fiscal year a stunning 12% of all new NINo registration of adult overseas nationals in London were accounted by Italians:
Please note this measure is possibly a very low estimation of immigration, as it doesn't take in account non working partners, children or other dependants that may migrate with the breadwinner. This is really as all the economically active inhabitants of one small Italian city, such as Ascoli Piceno or Mazara del Vallo or Rovigo, may have packed and moved in 12 months to London.
Update 2015 August 09
The London Datastore has moved the dataset used to build the diagram to a new location.