Aker announced the ambitious plan during a round table discussion in Norway with British Prime Minister David Cameron yesterday.
The Norwegian oil field services and product supplier, which employs more than 3000 people in the UK, opened a new office in west London last year. The office currently employs 200 workers.
"Based on this initial success and a highly favourable market outlook, we see that we have the potential to add a further 1300 employees by 2015," Aker chairman Øyvind Eriksen said.
"This is driven by activity in all key oil and gas regions worldwide."
Last month, Aker announced it was looking to grow its Aberdeen operations with 500 jobs over the next two years.
Cameron said Aker's decision to create the new jobs at the engineering hub in west London was great news for the local economy and a vote of confidence in the skill and expertise of the UK's engineering sector.
Eriksen said oil and gas engineers in London were typically experienced with an international mindset.
"By combining our own experience with this experience we can offer our customers engineering related to field architecture, products and technologies both in the North Sea and internationally."