Welcome to The Answerbank, Guthlac, but you seem to have started off with an impossible question to answer!
There's no such thing as 'the' Hardy family. In mediaeval times the name 'Hardi' (which evolved to become 'Hardy') was given to a person who was considered bold or courageous. So, even in those times, there would probably been lots of different Hardy families (all of whom were completely unrelated to members of the other families).
Further, over the years, there will have been lots of people called 'Trevor Hardy', so there's no way for us to know which one you're referring to. (For example, there were 43 people called 'Trevor Hardy' born in the UK in the first half of the 20th century, with probably loads more born in other English-speaking countries, such as the USA and Australia).
Similarly, in mediaeval times there could have been lots of unrelated people from Heywood in Lancashire who were assigned the surname 'Heywood' when they moved to elsewhere in the country, meaning that there became lots of different families using that surname.
So, as it stands, your question is meaningless. If you'd care to tell us exactly which Trevor Heywood your post refers to (e.g. by providing his date of birth or the names of his parents), then it might be possible for people here to investigate whether there are obvious links (e.g. through marriage) to anyone called Heywood.