A group called Just Stop Oil is blocking oil terminals across the country - including BP's Hamble Oil Terminal and Esso's Hythe Terminal in Hampshire.
The organisation said the actions are being carried out by supporters of Just Stop Oil as well as Extinction Rebellion - and that it had blocked "10 critical oil terminals".
Demonstrators are sitting on roads preventing tankers from leaving the sites.
The group claimed that more than 30 young people climbed on top of tankers at Navigator Terminals Thames in Essex.
Members of the two organisations are demanding an end to investing in oil, gas and coal.
'Fed up with a government burning your future - join us on the road,' the group tweeted.
ExxonMobil UK, one of the country's largest privately-owned underground oil pipeline distribution networks, confirmed demonstrations were under way at some of its sites on Friday.
Essex Police said they have made six arrests "so far."
The Esso Birmingham Fuel Terminal is among those targeted by the protesters.
Other protests are said to be taking place at Navigator and Grays in Essex, Buncefield in Hemel Hempstead and Birmingham's Esso terminal.
Police said they were responding to activists at a site in Tyburn, Birmingham.
West Midlands Police tweeted: 'We are working to deal with this as quickly as possible.'
The Just Stop Oil website says: "We must urgently end our reliance on fossil fuels to avoid irreversible changes in the earth's climate system."
The group says it wants action both in the short and long-term to reduce demand for fossil fuel energy - such as home insulation and renewable energy.
Demonstrations are expected across the country in the coming days over the cost-of-living crisis.
The People's Assembly has said it expects thousands of protesters will take to the streets tomorrow at various locations to highlight those suffering 'real hardships' due to the combination of rising fuel and food prices, inflation, and low pay.
ExxonMobil UK said it has suspended operations at its Hythe, Birmingham and West London fuel terminals.
Just Stop Oil supporters have disrupted Premier League football matches by running onto the pitch and tying themselves to goalposts in recent weeks.
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