Paul Standerwick, 36, was travelling to America for a family holiday with his wife and two sons when he moved seats to be next to his son so the pair could watch the landing by the window.
Speaking to ITV News, he said: "It wasn't until after we landed, actually, that someone tapped me on the shoulder and said the people sitting in the seats we moved to were moved on after they complained about bed bugs."
He said that he thought nothing of it at the time until he reached his hotel and "these horrible, itchy bites started to appear".
Mr Standerwick added: "They got really infected. Lots of pus. They were everywhere. On my neck, my back, shoulders and legs."
After contacting the airline, he said he was offered a £50 voucher.
Sharing photos of the bites on Twitter, Paul wrote: "BA #bedbugs left scars. £50 voucher - really!!?? Had these all over my body and legs!"
Mr Standerwick, from Sutton, south London, told the Daily Mirror: "I know mistakes happen but you expect a premium service from British Airways - and they haven't even apologised."
A BA spokesman said: "We have said sorry to our customers for their experience and appreciate it must have been upsetting."
They added: "Our customer relations has been in contact with the Standerwick family and have offered a gesture of goodwill."
15 flights from hell
15 flights from hell
We've heard of vomiting bugs in hotels and cruises but rarely on a plane. On a flight from Chile to Sydney in August 2013, 26 passengers became violently ill with gastroenteritis after celebrating at a festival in Brazil and picking up the bug before boarding the plane. Some of the passengers were taken to hospital once the plane landed in Sydney and the plane had to be quarantined and disinfected upon arrival. This is one flight we're really glad we weren't on as the Boeing 747-400 only had eight toilets and the group developed vomiting and diarrhoea.
When you're on a long (and pricey) trans-Atlantic flight, the one thing you don't want to happen is for the plane to run out of toilet paper. Unlucky for passengers on a United Airlines flight from London to San Francisco in June 2013, the toilets ran low on tissue after the airline forgot to restock its supply. The passengers were forced to use cocktail napkins instead of loo paper when nature called and were allegedly told to use what they had brought on board for the 10-hour flight. That's one way for an airline to find itself deep in poo!
We all hate flight delays and even a few hours can leave us peeved, but holidaymakers on a Monarch Airlines plane from Tenerife were stranded on the Canary Island for a whopping 50 hours in August 2012 when their plane suffered a fault. The crew discovered a problem with the door hatch and asked passengers to get off the plane and wait for three hours. They then spent another hour on the plane before being put up in a hotel. A replacement plane eventually flew them to Birmingham.
When a pilot accidentally locked himself in the toilet of a New York-bound flight in 2011, he ended up causing a mid-air 'terror' panic too. When a well-meaning passenger heard the pilot trying to get out of the loo, he offered to help. The pilot asked the man to go to the cockpit and inform the crew of the situation, but the co-pilot was completed spooked by the man's "thick Middle Eastern" accent and refused to let him in, calling a state of emergency. Fighter planes were alerted at the arrival airport and the co-pilot was told to "just get on the ground". When he managed to break out of the toilet the pilot assured air traffic control that there was no threat. But the FBI still waited to meet the plane when it landed and spoke to the poor passenger who just wanted to help.
If you're a non-smoker, you won't be able to think of anything worse than a smoker lighting up a cigarette next to you on a flight. Three Canadian passengers on a Sunwing flight did just that in February 2013 - even though smoking has been banned on aircrafts for more than 15 years. And what's more, they refused to put their cigarettes out and ended up diverting the flight, which was travelling from Halifax to the Dominican Republic, to Bermuda. When the plane landed, their passports were seized by police, while the other passengers continued their journey.
There are times when the pilots are up against nature and have absolutely no control over a situation, such as when lightning strikes. In January 2013, a Turkish Airlines flight carrying 114 passengers was struck by lightning. A passenger filmed the incident, which saw sparks from the plane's engine as it caught fire and the cabin lights flickering on and off. Fortunately, despite the plane catching fire mid-air, it made a safe emergency landing and no-one was injured.
One emergency landing is enough but could you handle two on one flight? That's what "terrified" passengers on a British Airways flight from Saudi Arabia to London endured in August 2013. First the plane was delayed for five hours and in the air for about 40 minutes before making an emergency landing because of a problem with the plane's wing flaps. Then the next day when the passengers boarded the same plane, the problem reoccurred and the flight was aborted a second time. Passengers were reportedly "physically sick and crying" during the landings as the plane had to circle the desert to dump around 20 tonnes of fuel to be the correct weight to land safely.
If the sound of babies crying on a flight is disruptive enough to your journey, you certainly wouldn't have enjoyed the American Airlines flight from Los Angeles to New York, which saw an "unruly" passenger repeatedly sing Whitney Houston's I Will Always Love You. We've watched the video and the woman is no Whitney Houston! She ended up being handcuffed and removed from the flight - but not before putting the other passengers off Whitney's music for life!
Thought a naughty child kicking your chair was bad? In August 2013, 30 adults created the flight from hell when they ran riot on a Ryanair flight from Prestwick to Ibiza, swearing, threatening and even sexually harassing crew in front of other holidaymakers, including families with young children. The men were warned by police about their behaviour before boarding but this didn't stop their drunken rampage, which saw them shouting and jumping on the seats too.