The organisation came to international attention 30 years ago when teams of protesters in speed-boats were filmed zipping across the bows of huge whaling vessels. Since then, Greenpeace has become concerned with issues as diverse as deforestation, genetic engineering, nuclear power, climate change and GM food.
'We don't do them all at the same time,' says Lee-Harwood. 'At any time we are only focusing on a maximum of two, and ideally one, campaigns. Our media strategy is based around a series of peaks rather than a baseline. We don't attempt to provide a sort of Greek chorus to the whole environmental debate.'
Journalists looking for comment on issues in which Greenpeace is not directly involved are often disappointed and Lee-Harwood admits this can lead to resentment.
Paul Brown, The Guardian environment correspondent, has no complaints: 'Blake is very reliable, very disciplined. When he does come to you, you know it's a story.'
The most recent 'peak' - which saw Greenpeace make national headlines earlier this month - has been based around timber. More than 40 activists entered the refurbished Cabinet Office in Whitehall, in hard hats and overalls and on the hunt for doors and window-frames made of sapele, an African wood that does not come from sustainable resources.
This summer, attention will turn to nuclear power. But the agenda can change quickly, Lee-Harwood says: 'Something that seemed the right idea ten months before may become inappropriate.'
Lee-Harwood oversees three PROs, one of whom is on semi-permanent loan to other Greenpeace offices around the world, most recently to Alaska and the Amazon. A flat structure in the London office means PR strategy is not only developed by his unit - which takes in the press office, web and audio/visual functions. Lines are blurred, with the campaigns, marketing and actions departments all involved: 'We don't recruit people as issue specialists. There is always a trade-off between the need for issue knowledge and the need for flexibility.'
Lee-Harwood is an unlikely-looking activist. Tall, lean and sandy-haired, he has the youthful air of a popular history lecturer. But he finds disruption where he can. When he was media relations head at the Royal Society for the Protection of Birds (RSPB), he enjoyed getting Daily Mail readers to care about the environment under cover of birdwatching. And Greenpeace is now attempting to broaden its appeal, he says: 'We are moving beyond "blokes in boats".'
Suits and ties will be more to the fore at conferences it is organising involving stakeholders such as business leaders, politicians and scientists.
But fans of more traditional activity will not be disappointed. Greenpeace will carry on trying to make oil giant Esso the high street villain of global warming, while raids on GM crop fields are likely to continue. The GM lobby is coming back, he says with something like relish. 'They are much smarter, with more resources and better PR than they had before.'
Greenpeace UK membership is on the up - vital since it is not funded by any outside body - and stands at 200,000, bringing in £5m. There have been PR hiccups, though Lee-Harwood seems more fazed by the recall of some supposedly eco-friendly mouse-mats - they contained potentially poisonous fungus - than he is by news that former Greenpeace stalwart Lord Melchett has started consultancy work for Burson-Marsteller.
'Greenpeace gets into the media because we are people who act rather than talk,' he says. This does not meet with universal approval. Dirk Hazell, CEO of the Environmental Services Association, which represents owners of the waste incinerators that Greenpeace regularly targets, says: 'In PR terms, Greenpeace is trading long-term gain for short-term triumph. It has had the benefit of the doubt from journalists but that is changing.'
It is certainly true that last week's action in the Thames Estuary did not get much media coverage. Lee-Harwood says: 'Ship actions just don't work for the media anymore, they see it as hackneyed. Greenpeace is an old brand and the level of cynicism about it is unbelievable. My job is to work around it, not moan about it.'