Spurs were sweating on clearance for the Real midfielder, who they were trying to sign for a cut-price £8million.
Manager Redknapp revealed he became aware of 27-year-old Van der Vaart's availability just two hours before the 6pm cut-off.
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Redknapp claimed the Holland star had been due to join Bayern Munich for £18million but the move broke down on Monday.
The Spurs boss also confirmed he had made an enquiry about Liverpool winger Ryan Babel but "never came close" to landing him.
Redknapp did, however, finally complete the signing of Croatia goalkeeper Stipe Pletikosa on a season-long loan from Spartak Moscow.
With most Barclays Premier League clubs keeping their chequebooks firmly closed, analysts Deloitte said total spending this summer was around ¦pound;350million - 22% down on last year.
Source: PA
Source: PA