The first picture was originally published in a French magazine.
Italian hardtop made by M.M. Fattori & Montani. According to the advert the hardtop "follows smoothly the lines of the MGA, thus giving it a typical Italian appearance".


It looks like custom side curtains that are tilted to match the angle on top of the door, and you may have to duck a little more to get your head under the edge of the roof.

Addendum 5 July 2015:
Photos below are courtesy of Mauro Lozza in Italy who now has this hardtop.



On 16 November 2017, Mauro Lozza wrote:
"After long time without finding any information, I found last month these 4 photos dated 1956 showing very well the Fattori & Montani hardtop. Give a look carefully to the side screens: the frame is chromed, the opening part is the front one and there are holes in the rear plastic part for ventilation".