In a vital test case, which could affect 13 other local authorities, the council are appealing a decision made by high court judge, Mr Justice Stanley Burnton, in October last year.
Roderick Cordara, for the council, said Mr Justice Burnton had 'erred in law' when coming to his decision and urged three appeal court judges to overturn it.
In a highly technical case, Customs and Excise effectively say a refund was paid through other means.
Mr Cordara said it wasn't in dispute that the council had made an error in its VAT returns, and hadn't realised 'supplies activity' was in fact exempt from tax.
A spokesman for the council declined to reveal exactly how much money Cardiff City Council can expect to reclaim if they win today's case, but put the figure at 'several hundred thousand pounds'.
If the council are successful, the total cost to Customs and Excise could be £2m as the 13 other local authorities would then pursue their claims.
Peter Mantle, for Customs and Excise, urged judges to dismiss the appeal.
Lord Justice Schiemann, Lady Justice Arden and Lord Justice Scott Baker are expected to reserve their decision at the end of the appeal, due to conclude today.
STRAND NEWS SERVICE