Visited my new dealer today who said the spots were on top and not under the paintwork. Could have been caused by tiny metal fragments landing on the car and got wet, resulting in rusting... (? where I would get tiny metal fragments from as we live in the country) He took a bit of a 3M polishing compound and was able to buff out the spots.
He recommended something like Auto Glym Super resin polish (He said T-Cut would be too harsh). So I am very relieved that's all it was.
I would recommend if you do have a white car you keep an eye on it. Better to catch it sooner than later...
PS. Saw a purple iQ today for the first time at the dealer.... And saw an silver one on the road, looked a bit ordinary... That is in my humble opinion.