I sometimes wish that the CVT had a true continuous option that we could use as a baseline for evaluating the gear shifting behaviour.
I'd say if your car won't go above 4th with a cold engine, even at motorway speeds, that's a fault. On the other hand, it would be reasonable if it selected a lower gear than usual until the engine heats up and can deliver its full power. I guess there aren't any motorways on the Isle Of Wight for you to try this out.
I'm in the north of England and in the recent very cold snap it did seem as if there was sometimes a short delay before it changed gears, but it did go up to 8th gear at motorway speeds.
Remember you can always override the gears if you don't like the ones it chooses. Pushing the gearstick left then up/down makes it choose a slightly higher/lower gear than it would otherwise use, or you can use the paddles to get exactly the ratio you want.