I think the strongest candidate is the article "464". The size is 17x24cm, which would seem to correspond very well with the size seen on-screen.
The next size up, "464 Bis" at 21x30cm (A4), is clearly too large.
The next size down, "463" at 15x21cm (A5), is also a strong candidate, but would seem to me to require that the actors have rather small hands...
Has anybody seen the actual prop IRL, or has any other firm data that nails its size down definitely?
It should also be noted that Luca Natalizia has a range of "replaceable journals" in that same product line. They're basically the same as the above, but with removable booklets. The main visual difference seems to be that the distance the leather overlaps the pages seems to be slightly greater, which, looking e.g. at the picture
Whovian posted above, might suggest that BBC used one of these "replaceable" models, rather than the standard one.
In that range, it's article "773" that corresponds to the 17x24cm size, and "772" to 15x21cm.