what difficulties might face the british in controlling such a large empire

What technologies might be needed to control such a large area

Long and dangerous voyages

Enticing British to colonize the empire
Lengthy times for communication
Diseases

Hostile natives

What technologies do you think might be needed?

Factories, new technologies for ships (Im not sure what they are called), weapons

Navigation technology (determination of longitude)

Good!

eat limes

"Lime-juicers"
avoid scurvy

white oak frames and planking and locust trunnels (tree nails)

LOL, could go on for hours.

steam boxes for plank bending.
oakum, pitch pine, eventually copper bottom paint

Archimedes screw pump, capstan, windlass, aft rudder on pintles with wheel, deadeyes and lanyards .....