Assumption is that the Bank have a legal charge in place over property A. If so, all net sale proceeds must be remitted to the Bank and then they release the charge. Decision to release any funds is with the Bank. In the current climate I wouldn't hold my breath on them agreeing to accept less than the full net proceeds in debt reduction.
No real change in my response. If any one of the properties held by the Bank as security is sold, the net proceeds will normaly be required to reduce the borrowings. Whether reduction is for loan A or loan B makes no real difference. All security effectivel covers all debt.