Private Cheryl James, from Llangollen, Denbighshire, was 18 when she was found with a bullet wound to her head in 1995.
Last year her parents won the right to a new inquest after an open verdict had been recorded.
Surrey Police has been asked to comment.
In February, police lawyers asked the coroner to consider whether the hearing should be held at the same time as any other future Deepcut inquests, which led to an adjournment in the case.
Her father Des James said: "It's insensitive that they're delaying it. It's been really tough for us getting to this point.
"I made the mistake of relaxing and thinking I could leave it to the legal process."
Surrey Police has previously denied the move is a delaying tactic and has been asked for a comment on Mr James' latest claims.
Previously, Surrey Police said it supported a "thorough inquest" into Pte James's death.
She was one of four soldiers found dead at Deepcut, in Camberley, between 1995 and 2002.
A Surrey Police investigation was launched into their deaths in 2002, after pressure from families who rejected suggestions the soldiers had committed suicide.
The family of a soldier found dead at Surrey's Deepcut army barracks has accused police of trying to stall a fresh inquest into her death.