Without a picture, a precise id is not possible, but from your description, the most likely candidate is a penny Scots (which is not the same thing as an English penny) 1547 or 1554.
obv: facing crowned portrait in circle +MARIA•D•G•REGINA •SCOTORVM or variant
rev: forked long cross, crowns and 5-leafed flowers in the corners in circle OPI...DVM...EDN...BVR
The legends stand for "Mary by the grace of god queen of Scots" and "city of Edinburgh". There are several varieties, mostly depending on the face, but since you don't mention the portrait I presume it is a bit worn.
Peter