Google must be pulling up some incorrect fares, although it does come to £798 on the BA website on those dates, depending on the times you book. If you're not desperate to fly BA then you can book a direct flight with Emirates for £698 through Travelbag - they usually do quite good flight + hotel deals too. If you look on Kayak, it's showing BA flights at £634, although that's booking through BudgetAir, and I've no idea how reliable they would be.

Cheapest option on kayak is £480, routing through Kiev with Ryanair and Air Dubai - one for the brave only i think, although apparently the connection is guaranteed by the Travel Agent (Kiwi Air).