ok..I think I finally found one. 168.004 1966 35.5 mm diameter Caliber 561 23xxxxxx Serial number Dating to 1966
Real but very beat up, not even worth half the asking price, actually not wroth considering at all in this condition.
Given the condition, apparent in your photos, I think the answer is to walk away and look elsewhere; for a better movement and better case. There are better watches available at a lesser price.
£1,500/$2,000 would be very expensive for an .004 dome dial in mint condition. That is dogleg pie-pan money. This watch has had something of a hard life. I suspect the dial also has a lot more spotting than the pictures show. Definitely keep your money and look for something better - if you have this kind of budget you should be able to find something really good with a little patience.