Supermarkets insist they will not change their policy on stocking Israeli goods, despite protests from pro-Palestinian activists.
Tesco and Sainsbury's have both been targeted by boycott protestors in the past few days. Tesco reported demos at 20 stores.
The supermarket chain, Britain's largest, currently stocks Israeli products such as Yarden wine, Osem soups and cakes, and as well as fresh produce.
It also stocks dates produced in the West Bank but has announced it is withdrawing them next month as part of a "regular product review".
A spokesman said: "We have no plans to change our policy on sourcing from Israel".
We label products clearly. Customers can make their own decisions
Pro-Palestinian activists tweeted that they had forced four Sainsbury's branches - in Whitechapel, Brixton, Brighton and Birmingham - to close on Saturday, showing photographs of at least five police officers guarding the front entrance of the store in Brixton. But Sainsbury's said that only the Birmingham and Brighton stores had been closed - both on police advice and for only 30 minutes.
Photographs on Twitter show protestors storming the premises and posing for photos splayed out on the supermarket floor while police and security guards look on.
In a statement, Sainsbury's promised that the disturbances would not affect the company's policy.
"We are a non-political organisation and source our own brand products according to the ability of the producer to meet our quality, safety and ethical standards," said a spokeswoman.
"We give our customers the opportunity to make their own decisions by labelling our own brand products clearly and accurately. We have approved suppliers in both Palestine and Israel but no current own-brand suppliers from Israeli settlements in the West Bank."
Marks and Spencer, Waitrose and Morrisons said their stores had not experienced any serious disruption.
M&S said: "There has only been minimal disruption to trade at our stores in recent weeks.
"There have been no changes to our policy. We do not take any products from the occupied territories - the West Bank, Golan Heights or Gaza.
"To ensure we have complete traceability we must be able to see exactly where we source all our products from. Therefore, we only source from areas that we can visit safely. This has been the case for a number of years."
Waitrose said their sourcing decisions were never politically motivated while Morrisons said they had not experience any protests and would continue to stock Israeli products.