welcome to the forum!
Congratulations on your purchase!
Well firstly it sounds like its a good car if it made it back from eastbourne without any problems, and yes its VERY common to get a bit of milky oil in the oil filler cap. Give it a good un and see if t comes back. I had exactly the same problem and after a good run it didnt come back. Its just condensation which doenst clear if the engine isnt heated up for long enough. ( a tiny droplet of water can make the oil look very milky) but i dont think there should be any in the header tank? as this would mean oil has gt into the coolant system.
just make sure it never goes into the red on your temp gauge,
You ahve to remember with these cars, they have these niggly faults you will learnt your own tricks and tweaks to get it running exactly how you want.
Kind regards and welcome to the forum
Chris