That is only 210 W. No problem at all.
I had just a single, very low, light socket in my bathroom.
Very dangerous when getting in and out of the bath.
I diverted the wires either side to fix 100W bulds on oposite walls.
I used a wire connector box were the old socket was and diverted the wires either side. No Problem at all.
The council electrician came to check it out and passed it without a problem.
When you think that all your house lights can be on at the same time on just a 5A fuse-box fuse then you realise that the system can take more than you actually think.
How often do you have every single light in your house on at the same time. Very rare in deed. Frontroom 100W, Livingroom 100W, Kitchen 100W, Hallway 100W, downstairs toilet 100W, Landing 100W, bathroom 100W, Upstairs toilet 100W, Master bedroom 100W, little bedroom 100W,
closet 100W. That's 1100W and I am sure that each area can accept 120W bulbs, so do not worry at all.
Just make sure that you use sealant around the recess lights to STOP steam/condensation getting to the wires and causing a possible fuse blow.