One of the issues you are going to face, being "only" separated, is the uncertainty of what is going to happen due to the eventual divorce. In other words, are you going to be told to pay child support or alimony; for what amounts; which debts are you going to have to take on and which will your spouse? With all this uncertainty, lenders are going to be reluctant to give an approval.
This is in addition to the answers below. You will need your spouse (you are still married) to sign on the loan or sign-off on the disclaimer, if you can get approved. Remember, not telling your full financial story is committing mortgage fraud.