About 1,000 farmers gathered in Bridgwater to protest against the price supermarkets pays for milk.
Tractors blockaded the entrance to the Morrisons Distribution Centre near junction 23 of the M5 motorway.
Farmers say it costs more to produce each pint of milk than the price they are paid for it.
The supermarket has announced it will meet farming industry leaders next week to discuss milk prices following the protest, and others in the UK.
James Hole, of Farmers for Action, who was one of the organisers of the protest, said: "These [farmers] want to stand up and fight for their future and make sure they have a sustainable price for a sustainable future.
"We are struggling, we are working as hard as we can to get results within weeks. We haven't got months.
"These guys are really worried about whether or not they'll make this winter and have enough money to go around to keep the cows."
Arla, Britain's biggest milk co-operative, previously said it was cutting the price of milk by 0.8p per litre, making a litre cost 23.01p.
Many farmers say that amount is not enough for them to make a profit, estimating it costs between 30p and 32p to produce each litre.
A spokesman for Morrisons said: "We are disappointed with the disruption being caused to our stores and our customers.
"We recognise that the current issue is being caused by a reduction in global demand for milk that has led to an over-supply in the UK and very difficult conditions for many dairy farmers.
"We want to reiterate that we are not seeking any further reductions in milk prices and we will continue our talks with the National Farmers Union, in a constructive manner, to finalise our agreed plan of action."
Other similar protests have been held in other parts of the UK in recent days.