I don't live in the UK. I live in Wisconsin where the spring and summers can be downright muggy, and the very cold winters dryer than the Sahara--literally.
All of my ukuleles are solid wood. Some are very sensitive to changes in humidity, others shrug it off without a problem. I keep them mostly in their cases with a Boveda/D'Addario HumidiPak. The HumidiPak keeps the humidity level in the case at about 45 percent according to the hygrometers. They absorb excess humidity and release moisture when it's too dry. The only downside is having to replace them every year.
The wood inside of your uke, and the fretboard is usually not finished. They breathe. Taking in moisture and losing it. It doesn't usually happen rapidly. And, the denser the wood, the slower the process. If the wood is properly dried and aged, it becomes pretty stable. But all wood expands and contracts with changes in humidity. And to a lesser extent temperature. Extremes in either are a problem. Rapid changes are a problem. Steady, consistent humidity and temperature is the ideal.
Don't worry, if you leave your uke out of its case for a couple of days, or even a week or two in the warmer, humid months, you shouldn't have a problem. In the hot sun, or a hot car, or a desert, you might.