Aviation law currently blocks Sussex Police access to some Air Accidents Investigation Branch (AAIB) material relating to the crash, last August.
The force is required to take the transport secretary to court so the material can be released.
A Hawker Hunter plane crashed into spectators watching the airshow from the A27 last August, killing 11 people.
Det Ch Insp Paul Rymarz, who is leading the investigation, said: "The application is to enable Sussex Police to obtain access to legally protected material including cockpit recorders and footage, expert reports and some documentation."
Mr Rymarz told a pre-inquest hearing in March their inquiry "cannot progress effectively" until the High Court issues its ruling, in a hearing scheduled for 14 and 15 July.
Without this material "key evidence is missing and experts are not in a position to provide interpretations", he said.
The pilot, Andrew Hill, 51, survived and has been interviewed under caution.
A spokesman for the AAIB told the pre-inquest hearing its final report was expected to be published in "early summer".
Investigators of the Shoreham air crash are to get a bid to access evidence heard at the High Court.