Well, the OP wants a BRITISH empire, so we might not want TOO much in the way of Scandinavian possessions.
In particular, owning Denmark is likely to get this empire involved in continental European, especially Baltic, affairs. That COULD give you a thalassocratic empire, but it would be a pretty limited one.
On the other hand, it's possible that if England doesn't have any Scandinavian possessions, they'll be focussed on the British isles to the exclusion of maritime power.
So.... Enland+Norway. Lots of shipping, little continental involvement.
Once Vinland is discovered, England/Norway might use it as a colony, younger sons wanting land of their own, population pressure, etc.
As for shipping, knarrs were adequate to the task (barely), and could be developed further.
Once you have an empire consisting of England, Norway and a dozen (hmmm.... 13?) colonies in North America, that would serve as a good basis for future growth.