The Garden Museum is an independent charity with 12 paid staff and a board of 15 voluntarily trustees.
The museum is housed in a medieval church next door to Lambeth Palace and is the only one in the UK for the history of gardens.
It generates 95 per cent of its income itself, a sum which has doubled in the last five years through a new space for exhibitions and events built in 2008.
In October 2015 it expects to begin building a £6.6 million development. So far £5.7 million has been raised, with £3.5 million from the Heritage Lottery Fund and £2.2 million in pledges from trusts and individuals.
The Garden Museum said: "The commercial success of the new development is fundamental, as increasing revenue by a further 50 per cent will give stable funding for an expanded programme of education, acquisitions, and exhibitions."
The treasurer will be supported by a full-time finance manager and a part-time head of finance. The Tteasurer will give his or her fellow Trustees a concise overview of the museum’s performance at board meetings four times per year, and attend an executive sub-committee once per month.
The museum said: "The key challenge at the moment is to balance the on-going operations of the Museum with the resources required for the imminent capital project."
Capital Gardens owner and Garden Museum vice-chairman Colin Campbell-Preston is vetting candidates.