Hi Gordon, i have just checked a spare pair of shoes that i have and the pivot hole is 12mm as you say, they also have only one return spring between them instead of the usual two, they have "Made in Italy " embossed on them, but no part number. I did not have to make any changes to the brake plate, the new shoes fitted straight on. I have found the receipt for my shoes and it states that they are Lambretta, to fit models LI, TV, GT and SX all from 1959 onwards. Hope this will help you source some. As a last resort you could have your shoes relined, this is what i now do and keep rotating my spare set whilst the worn ones are away.
Regards Steve.