It was not until a landmine damaged Broadcasting House during the Second World War that the BBC began its residence here, with the European Service moving in. The rest of the Overseas Service followed in 1958.
The building has previously been owned by the Church of Wales and the Post Office and the BBC now leases it from a Japanese company, Kato Kagaku. This lease expires next year, so Bush House's days as the home of the World Service are limited. The BBC has set out plans to move the World Service to Broadcasting House, but they change their minds about these plans so often, who can be sure. Wikipedia reports rumour that the LSE may move in when the BBC has gone. Alongside the BBC, the building is home to a very small arcade of shops including a specialist pen shop.
For more information, see http://www.bbc.co.uk/historyofthebbc/collections/buildings/bush_house.shtml