Small Flat Washers
While I am not the original owner of my Mk II, I have owned it since mid-1970. The shroud "flange" has two small diameter screws going though it with two or three (I can't remember off hand) small flat washers under the "flange".
Having said this, I checked the Rootes Tiger 260 and 289 Parts Supplement Manual to see what it shows. It seems to call the shroud a "radiator cowl". In Section TF - Radiator has a diagram of the radiator and many parts, but does not show this "flange" or the two small screws or bolts which attach it to the body. However, in the list of parts, it refers to the following parts needed to attach the "radiator cowl" to the body:
2 Clip
2 Screw, #10 UNF x 3/4"
2 Rivnut
See the attached Snip of the appropriate section from the parts manual.
PS - I need to check my car in the morning. As I recall, there were a couple of clips on top of the shroud, clipping the upward part of the flange to another part of the shroud. Sorry I cannot be more exact, as I am working off my (poor) memory.