A really remarkable piece of work. But I hope I may be forgiven for thinking there may be a typographical error in the description.
It sure looks like a seventeenth-century ship (i.e., one dating from the 1600s). There were no ships of 64 guns in the English navy (or, to my knowledge, anybody else's) during the sixteenth century, and the term "ship of the line" wasn't in use yet. (I just took a look at the latest book on the subject, Arthur Nelson's The Tudor Navy, 1485-1603. I did find, on one of Mr. Nelson's ship lists, one vessel of 68 guns - but that was a freakishly large galleon, Sir Martin Frobisher's Triumph.) The rating system (identifying this one as a "third rate") didn't come into use until the 1630s.
To get really technical about it, the term "sixteenth-century British" is a bit of an oxymoron in itself. The kingdom of Great Britain didn't exist until 1707, when the Act of Union brought Scotland under the same Parliament as England and Wales. Prior to that time the institution that operated ships like this was known as the English Navy.
If it's not to late, you might want to think about the flag that's flying from the main masthead. The English/British flag has evolved considerably over time. My monitor is too small for me to see it really clearly, but it looks like the one on the model may have the St. Patrick's Saltire - the diagonal red stripes. They weren't added to the British flag until 1801, when another Act of Union brought Ireland into the fold. Prior to that time the diagonal stripes were white. The St. Patrick's Saltire is, in effect, a pinwheel-shaped diagonal red cross superimposed on the slightly wider diagonal white Cross of St. Andrew, representing Scotland. (The ensign flown by English warships of the seventeenth century did include the Cross of St. Andrew - even before the 1707 Act of Union. That's probably the flag that would be appropriate for this model.) In the sixteenth century flag heraldry had yet to be firmly standardized, but the most common flag flown by English warships at that time seems to have been the simple red Cross of St. George on a white background.
Please forgive this bit of pendantry from a history teacher (who's about to go to bed, having stayed up too late for his own good grading exam papers). Like I said earlier, I suspect the date is a simple typo. I wouldn't mention it if it weren't easy to fix. And welcome to the Forum. You'll find it's a nice, helpful place - except for certain obnoxious, long-winded history teacher types.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.