According to the site:
Some new filming news on the Harry Potter and the Half-Blood Prince movie has appeared online which details that construction started this week on the cloisters and gardens of Gloucester Cathedral and that Malfoy’s house is under construction.
New for April 2008 is an update on the filming taking place at Leavesden Studios for Harry Potter And The Half Blood Prince. We know they have filmed Dumbledore’s death and the Quidditch has also been filmed, which might explain why the cranes are now gone. We also know that the Malfoy’s house is under construction.
Also a report from a visit to the set in early March indicates that Dumbledore's death scene has already been filmed.