The system has to have enough capacity to meet peak demand allowing for some plant to be down for maintenance at any time. Since the demand is very much less than peak for most of  the time much of the plant is stood off at any one time. To minimise cost the plant with the highest incremental generation costs is stood off first. As the load drops further progressively more expensive generation is stood off. This means that nuclear generation that has very low incremental costs (but enormous fixed costs) is run almost flat out all the time. Likewise any wind generated power available is accepted as it has almost zero incremental cost.

The swing to coal from gas generation is thus accounted for by  the least efficient of the gas generation being more expensive now than the most efficient of the coal generation. What you describe as a big jet engine coupled to a steam turbine is a combined cycle system and can run at up to 60% thermal efficiency. There are still a fair number of stations that are, in your terms, just a big jet engine. These have efficiencies down to 45%. With the best of coal fired generation at 40% efficiency it does not take much of a swing in the relative costs of coal and gas for the gas generation to be stood down first.

Although Wytch Farm accounts for 90% of the 60 million tons of oil that has been extracted from onshore UK sites the DTI lists 30 other tiny onshore wells. These are scattered over the country which implies that there must have been a fair bit of survey work done.

Not usually included in UK oil resources but nevertheless economically important is the London Clay used for making Felton bricks. The clay contains too little oil to make it worth extracting but just enough to allow the bricks to self fire by careful management of groups of ovens with the heat of adjacent ovens bringing each new batch up to the temperature at which the oil starts to burn without the need for external energy input. This clay is almost unique to the UK.