Thanks very much espro_o5 - worked for me. I went into Control Panel - Administrative Tools - Services. Right clicked the SQL Server Analysis Services (MSSQLSERVER) service, selected Properties and on the Log On tab select Local System account. Back in the Services list I restarted SQL Server Analysis Services and after that the deployment of the cube from Business Intelligence Development Studio worked fine.
Would have taken me 1000 years to find that issue, if ever.