To answer OP's question - yes workplace sickness will increase if we cannot adapt. The UK is humid. and humidity matters.
The body stays around 37°C by getting rid of excess heat. It regulates by sweating, but if the air is already full of moisture sweat evaporates slowly or not at all. Meaning the body cannot maintain that 37°C which is critical.
You don't go from "completely fine" to "hospitalised with heatstroke" - obviously it is a progression back and forth between stages and generally stresses the body out bringing out other vulnerabilities and illnesses, (this is where workplace sicknesses are likely to show up)
The body first tries to compensate: you sweat more, your heart rate increases, and you feel hotter and more tired. Your heart then has to work harder to pump more blood to the skin, while you are also losing fluid and salts through sweating. As dehydration and heat build, you can develop heat stress thirst, headache, fatigue, irritability, dizziness, reduced concentration, and feeling weak. - this describes most of us this past month! 😂
If the heat continues, this can progress to heat exhaustion: (not heat stroke yet) heavy sweating, nausea, weakness, faintness, and feeling unable to carry on.
Heatstroke is the point where the body's temperature regulation starts to catastrophically fail. Sweating may stop, confusion can occur, coordination can deteriorate, and the high core temperature begins damaging organs. It is a medical emergency. People end up in ICU.
All because sweating in humidity is not effective.
Humidity matters. So tired of hearing "but people who live in hot countries!!!" (yes Sandra... a hot DRY country, with an AC culture to boot and/or houses that were build to expel heat not retain it)
Fun fact - it's why dogs are at a higher risk of heatstroke because they don't sweat. They pant, which is even less effective than pointless sweating