Plans for an ambitious transatlantic trade deal have been launched by the European Union and the United States.

Negotiations will begin in Washington next month amid hopes of a speedy agreement that will help the world economy grow more rapidly.

Announcing the launch of talks, David Cameron said a successful deal would add up to £100bn ($157bn) to the EU economy and up to £85bn ($134bn) to the US economy.

"This is a once-in-a-generation prize and it must be seized," the prime minister said.

UK sources said that it was hoped the negotiations could be wrapped up within 18 months, but US president Barack Obama warned that there would be difficulties to overcome.

"This is a priority for the United States" the president said. "We will give negotiators a strong mandate but we will have to intervene to break through logjams."

France has already insisted that cultural industries are excluded from the negotiations, fearful that it would increase the influence of Hollywood.

Obama said: "We must resist the temptation to downsize our ambitions and avoid the difficult issues just get a deal."

José Manuel Barroso, president of the European commission, said: "Negotiations might not always be easy but they will be worth it. We will find solutions to thorny issues, we will keep our eyes on the prize and we will succeed. We intend to move forward fast."

Cameron has made trade liberalisation one of the main themes of the G8 summit and said that a deal would mean extra jobs, lower prices and more choice. UK officials said an agreement could boost British trade by £10bn – worth £380 for each household.

The prime minister said it would be the biggest bilateral trade deal in history and "have a greater impact than all the other trade deals on the table put together", creating up to two million jobs.

He added: "The whole point is to fire up our economies and drive growth and prosperity around the world. To do things that make a real difference to people's lives. And there is no more powerful way to achieve that than by boosting trade."

The US president said: "The US-EU relationship is the largest in the world. We trade about $1tn in goods and services each year, we invest nearly $4tn in each others' economies and all that supports around 10 million jobs on each side of the Atlantic. This potential ground-breaking partnership would deepen those ties."

Although much transatlantic trade is already tariff-free, there are a number of sectors – such as financial services – where officials believe there is scope for liberalisation.

Washington and Brussels have warmed to the idea of a trade and investment partnership following the prolonged impasse in global free-trade talks, now into their 12th year.