Perhaps the 'round orange component' is a translucent coolant reservoir with orange coolant fluid? Lots of visible steam suggests an overheated engine. If it was because of a coolant leak, there wouldn't be any orange fluid left to be seen in the reservoir. So despite my complete ignorance of the underbonnet and coolant colour of an old Mini, my expensive working diagnosis is a failed cylinder head gasket, possibly because it's got hardly any oil in it.......

OP says he just had a service so prob not run out of oil.

It is not unknown for a distracted mechanic to fail to refill it, although unless it's a Honda I doubt if it would manage 100 miles on an empty sump - although with an old loose engine you never know.....

But I agree,.....

Go back to the people who serviced it