This was actually a topic raised in the Fennell Report into the 1987 King's Cross fire which killed 31 people, including one fireman.

Without modern synthetic flame-retardant materials, wool is actually a fairly good choice for a firefighter's protective gear. Strong, durable and insulating, wool is also naturally flame-resistant due to its high nitrogen and water content. That's not to say it doesn't burn, but it is much harder to burn. Unlike synthetic fibres, wool tends to smoulder when it does eventually catch fire, unlike synthetics which tend to melt and then adhere to skin. If you're from the UK, you may remember a prominent media case a few years ago when TV presenter Claudia Winkleman's daughter was left with severe burns when a Halloween costume caught fire and melted to her skin. In fact, wool's fire resistant properties mean that it's still used today as fire-protective clothing as well as home insulation. You might notice that F1 drivers typically wear woollen undergarments under their race suits, and such garb is also common for modern firefighters and police. Wool is also commonly woven into modern flame-retardant protective gear.

The problem with wool is that, while it's initially water resistant and insulating, when it gets wet enough, it gets very wet, and thus very heavy, unwieldy and cold. For firefighters directing large volumes of water, potentially on a cold night, this is understandably a problem, hence the introduction of the plastic/rubber trousers. As the Fennell Report states, a key problem for firefighters at King's Cross was that their 'protective clothing' was largely designed to stop them getting too wet rather than to protect from anything but brief exposure to flames. After all, it was deemed that firefighters would only need to enter a burning building in extremis, and even then only briefly - say to carry out a casualty - rather than necessarily spend a prolonged period in a sustained fire such as at King's Cross.