I went into Caffe Vergnano (a chain of coffee shops in London), and my cuppa was prepared with the following device:
From a rudimentary inspection, it seemed to be an arcanely constructed espresso machine, but is there something special about it?
Elektra Belle Epoque P1C:
See this page: http://www.elektrasrl.com/belle_epoque_2grel_cr.php
You can still buy these, they are very expensive of course, I don't think there is anything particularly special other than the design and finish: http://www.elektrasrl.com/belle_epoque_details.php
The home version is this one: http://www.elektrasrl.com/fam_retro_1grsa_c_a1c.php
Which will set you back over 1000 English pounds: http://www.myespresso.co.uk/product.php/27/elektra-mini-verticale-semi-automatic-espresso-machine---chrome
You may be wondering how come I answered this so quickly, it is because I have also been to the very same cafe you showed, the one on shaftesbury avenue, and was intrigued myself. The finish of the machine is hand made so it takes time for one to be delivered to you. I don't think there is anything particularly special about it but one of the nice things is the internal covered area for storing and warming cups. The internal guts are no different to other modern espresso machines.