Phonogram UK released some Dire Straits tracks on the unique 10-Inch / 25-CM size. All records are UK-made and play at 45 rpm. It is a record-format between the 7-Inch and the 12-Inch variants.
In the 1950s there are a lot of 10-Inch LP-Albums released in USA, in UK and in Germany, too. Some 1980s bands released some of their singles also on the 10-Inch format.
They are not so rare and you can get them in pristine condition for reasonable prices. The best chance to get them is in the UK, where they had been manufactured in the mid eighties.
Phonogram Vertigo UK released the following Dire Straits songs on the 10-inch format:
Dire Straits - Private investigations/Badges, Posters, Stickers and T-Shirts - DSTR-101, 1982
Dire Straits - Love over gold-Live/Solid rock-Live - DSTR-610, 1984
Dire Straits - So far away/Walk of life - DSTR-910, 1985
Dire Straits - Money for nothing/Love over gold-Live - DSTR-1010, 1985
Dire Straits - Brothers in arms/Going Home-Live - DSTR-1110, 1985
That´s it by Dire Straits. There are no more 10-inch releases known by official record-companies.
Maybe it depended on the record-company and the band, or the song, if a release was planned on the 10-inch format.