Little Details

Without a reason to be there particularly, if you want them to travel by ship, I'm not sure that it would make sense to ride to King's Lynn first rather than simply sail from London, itself a substantial port. Even if they couldn't get passage on a ship all the way to Berwick, theyd be able to get one some distance. However, by 1590 there is also a well-established road for your journey, the Great North Road covering the journey from London to Edinburgh, generally via Berwick, so they can simply travel by land if you want. You're about 60 years too early for stage coaches, though by this time private coaches did exist in England, but they could also ride. There were inns at the towns en route.