El Al has suspended its flights "until further notice".
All flights between Britain and Israel have been cancelled.
The disruption follows a decision by workers at El Al, Arkia, and Israir airlines to begin an "open-ended" strike yesterday, with the Histadrut labour union supporting them.
The strike is a protest against the Open Skies policy that allows more foreign airlines into Israel.
The agreement was struck with the European Union to allow a variety of carriers to fly into Israel and allow Israeli flights into the EU.
The agreement, which was overwhelmingly approved in the Knesset, is designed to improve competition and bring down fares to Israel.
But the airline union claims it will cost Israeli jobs.
A union spokesperson said: "Israeli citizens will not support a deal that will sacrifice the incomes of thousands of families just to please foreign carriers."