In defence of Just Stop Oil, they are not campaigning for the immediate abolition of the use of oil (fossil) fuels, which would take the UK back to the dark-ages – but are against the extraction of new oil and gas resources. How much of an impact this would have on the production of oil & gas, I don’t know.
But they also want a rapid transition to a low energy, low carbon world – so if they were to get the government to halt the extraction of new fossil fuel resources, they would target other fossil fuel use to meet their aims.
The world is currently burning through around 100 million barrels of oil a day, and it is projected to remain at around this level through to the middle of this century, only then reducing as alternate energy sources come into wide-spread use.
Whether a continuance of burning such an amount of fossil fuels will cause a global warming catastrophe is open to debate – but at least you are a little more informed on Just Stop Oil and their objectives.