Mr McCully denied it would affect New Zealand's foreign policy stance, saying it was a practical arrangement.
"I'm talking about simply sharing buildings and some core services. [Mr Hague] has been quite assertive about how much value there is in getting efficiencies in that way and I think he's right about that, actually."
Mr McCully said New Zealand already had a similar arrangement with Australia, subletting office space at the Australian Embassy in Vienna.
Britain has started expanding its representation in South American and African countries, as well as the Middle East - all areas in New Zealand's sights as it seeks to tap into broader trade markets.
Mr McCully said Mr Hague's visit was his second in two years.
He said the pair would also discuss recent developments in Fiji, where interim Prime Minister Frank Bainimarama has rejected a draft constitution prepared by a constitution commission partly funded by $500,000 from New Zealand.