Re: The UK mostly powered by coal?
Your coal based power plant throws away vast amounts of heat
As do gas turbines. Running in combined cycle operation efficiency is better (c58%, cf c52% for older coal plants) and so waste heat is less from CCGT than from coal, but its still there. Unfortunately, the panicked adoption of renewables has added all manner of intermittent generation to the grid, and requires the CCGT to do far more peaky operation, that earns lower overall income. The heat recovery plant for combined cycle operation then isn't always economic to run, because it is fundamentally a parasitic load that needs long spells of continuous operation to make economic. So quite a few UK CCGT aren't running in combined cycle mode even though they have the plant to do it, and when running in open cycle mode they have similar thermal efficiency to a coal plant, and similar heat losses. That isn't as apparent because the cooling medium is the exhaust gases, and therefore there's no need for huge cooling towers and plumes of water vapour. But its still being wasted.
If you can re-use the lower grade waste heat from a CCGT for an industrial process, then you can see plant thermal efficiency rising to 75% (eg the Isle of Grain CCGT, when pumping heat to the National Grid LNG terminal). But that's a niche case, requires the gas turbine running long enough to make the combined cycle economic, heat networks are wildly expensive, and use cases for low grade heat are few and far between. Even Grain CCGT isn't able to achieve that 75% very often, because the LNG demands are very intermittent, and may not coincide with times when the CCGT is running for electricity. My boss at that time was an engineering director who had commissioning and asset management accountability for Grain CCGT; I can assure you that there's no way that the plant would have been built if the pre-investment models had accurately predicted the operating environment, load factors, and wholesale prices. Which is why, despite the need for new build plant, there's no big queue of people wanting to build them.