The Immigration Services Union says that at least 80% of its members have joined the national day of action.
But Heathrow and other airports say there are no significant immigration delays.
The UK Border Agency said its contingency planning, involving volunteers from other parts of government, had minimised delays.
Lucy Morton of the Immigration Services Union says officials estimate that between 80 and 90% of members have turned out for the strike.
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Early signs show our contingency plans are minimising the impact of strike action, but waiting times at some ports may still be slightly longer than normal”
UK Border Agency
She said that 22 of 23 staff had not turned up to work at Calais and as far as they were aware no staff had gone to Heathrow. Some 4,500 of the 6,000 UK Border Agency staff are union members.
Ms Morton said the union understood that delays were not significant at Heathrow because airlines had reduced their capacity.
That airport, one of the world’s busiest, is publishing regular tweets on the situation across all its five terminals but has so far seen no delays.
A UK Border Agency spokesman declined to give details on the number of staff working at ports but said: “The security of the UK border remains our top priority and we are working hard to manage any disruption throughout the day.
“Early signs show our contingency plans are minimising the impact of strike action, but waiting times at some ports may still be slightly longer than normal.”
The government had considered calling on the army to help manage the border, but found sufficient volunteers from overseas embassies and other departments.
Passengers arriving during the morning at Heathrow saw a marquee and rows of chairs and portable toilets set up to deal with possible overcrowding.
The UK’s second busiest airport, Gatwick, has reported no delays, with some passengers describing immigration as quicker than normal.
Stansted, north of London, is also operating without abnormal queues and investigators have seized a 1.5kg consignment of cocaine.
The Port of Dover in Kent said services to Calais and Dunkirk were “running well and to time”, with no queues on approach roads.
The Public and Commercial Services (PCS) union, which also has members inside the immigration service, said the border was being staffed by a “hastily gathered” group of police officers, private contractors and volunteers with little training. It said 90% of its members had walked out.
Pete Norris, PCS branch secretary for the south-east of England, said: “We have been out on the picket line since last night because of our night shifts and we have seen literally one or two of our members go into work out of what would normally be about 1,000 staff.
“We have had job cuts of up to 25%, a pay freeze for the past two years but our main problem is over our pensions.”
Bristol Airport is also reported to be running normally but the Torpoint ferry crossing, between Devon and Cornwall, is closed. The Dartmouth Lower Ferry, operated by South Hams District Council, has also been stopped.