I was in this situation before.I was only allowed draw down if I was beyond sale agreed and had signed exchanged and enforceable contracts.
The sale fell out of bed at signing time but we got sale agreed with another purchaser very quickly,
We asked bank could we draw down at sale agreed but got a very blunt NO and there was no scope for wiggle room.
Thankfully we got our signatures and , successfully drew down and completed but until you get beyond sale agreed the ink on exchanged contracts and the non refundable deposit in the paw they wont let you proceed.