In German sources frying is done with lard, butter, clarified butter and occasionally with suet. Plant oils are rarely used and can often not be identified because the texts just mention "oil". But archaeological records, toll rolls and other written sources show that there has been used a great variety of oilplants: expensive imported olive-oil, rape seed oil, nut-oils (hazle and walnut), line seed oil, hemp-oil, expensive sesam-oil, colza oil for example. In northern Germany, more closely to the coast, train oil, fish oil, whale fat, seal fat and such are recorded but there are no recipes which mention them. The production and availability of plant oils could not satisfy the demand. This seems to be one of the reasons for the late medieval "Butterbriefe" - popal permissions for the consumption of animal fat on fasting days and in Lent.
I don't know the situation in Britain as good as in Germany, but I would expect mostly about the same. Except for olive oil. It seems to me, judging from the relatively small quantity of English recipes I have read, that olive oil was more readily available and not that expensive as in Germany - and therefore used more often.