His profile has risen considerably over the past 12 months thanks to two things. Firstly, on the BBC television series The Museum of Life, shown this spring, he was able to promote the less well-known plant work of the National History Museum.
"It's too early to say what the impact of the show has been," he says. "But visitor numbers have increased massively - by hundreds of thousands." Indeed, most recent figures for the first part of this year show a 30 per cent increase over 2009.
The other big boost, both to the museum and to Spencer in particular, has been the opening last September of the £78m Darwin Centre. The eight-storey cocoon serves as a new home to the museum's plant and animal specimens, while giving visitors the opportunity to see the museum's scientists at work.
"We have done it will bells on," says Spencer, who devoted two years to developing the centre's content. "It's not to everyone's liking and some things have not turned out quite as we planned, but the reaction is often: 'We never had any idea you did all this,' which is one of the main things we wanted to achieve."
The centre houses the British Isles plant collection. Many of the contents date back more 300 years, including specimens collected by Linnaeus himself. "I have to ensure their well-being and enable researchers and the public to have access to them," says Spencer. "There's also communicating with the public about the museum's work - I'm a talking head in that sense."
Like all Government-funded institutions, the museum faces cuts to its £45m grant and has drawn up proposals to cut £2.3m in costs while making up to 40 staff redundant. "We have to give careful consideration to who we are and what we do," he says, guardedly. "I have contributed to that but the decisions will be made elsewhere. Everyone will know a lot more after the Government spending review. But when it comes to saving money, natural history is pretty low down the list of priorities."
However, he is more vocal on the role of plants and the public's understanding of them, which he thinks is woeful. "Plants are less obviously exciting or charismatic and will never be everyone's cup of tea," he says. "But if you don't familiarise children with what's in their garden, they will never know if it's for them. People who would have gone into it given the chance have become disenfranchised from the natural world - and when you lose the students, you lose the teachers. We have got into a cul-de-sac and, in the current economic climate, it will go further before it improves."
Yet the need for skilled naturalists has never been greater, he argues. "The level of skill we will need to understand the natural world in the next 20 years - in terms of climate change, invasive species and environmental degradation - is huge. When we realise the economic value of biodiversity to human health and well-being there will be a panic to redress the imbalance."
Putting this right starts in schools, he says. "We have to make a significant shift to integrate (whole-organism science) into the curriculum to enable students to appreciate it. Natural history can be used to teach other subjects and vice versa. But we have the deplorable situation of having very few teachers who know about the natural world.
"Even if the Government decided to put natural history on the primary curriculum, how would it do so with teachers who don't have the basic skills? They are often terrified of the natural world - they scream at the sight of insects and tell the children 'don't touch'. The whole point is to engage them, but when people are frightened of handling soil, then we have a problem."
The situation is no better in higher education, he complains. "The Government has pushed university departments more and more towards applied work like genetics and pharmacology. There are numerous examples of (natural science bodies) being run into the ground."
Spencer speaks with some bitterness from his own experience, describing his PhD at the University of Reading, on water moulds, as one of the last of its kind. "I am now one of the last people in the world still doing that sort of work," he says.
"Reading was one of the best in the world for those things, but it's virtually all gone now - the undergraduate teaching has closed, the herbarium will close. It's a bloody disaster."
Does he not take consolation, though, from the booming number of visitors to his own institution? "They are flooding in here and Eden and Kew, but it's treated like Disneyland," he says. "It creates wonder, excitement, even awe, but that's as much as we can do because the other pieces of the puzzle are missing. They have lost the fundaments of understanding and won't get that back by coming here once or twice in their lives."
1989-90: Horticulture diploma (incomplete), Kew
1990-92: Bar manager
1992-95: Personel officer, Kingsway College, London
1995-2002: Degree, then PhD in botany, University of Reading
2002-04: Field botanist, London Wildlife Trust
2004-06: Research assistant, Linnaean plant typification project, Natural History Museum
2006 to date: Curator, British, Irish & Sloane Herbariums, Natural History Museum.