It depends on several factors.
For remortgages lenders will typically expect the license to be in place on the basis there’s no excuse for it not to be.
If however there’s evidence the council are particularly slow then they may accept confirmation of the application and payment of the fee.
You’ve more chance of this being accepted if you have an existing license with the same council.
If it’s as a result of the recent changes lenders are more forgiving. However if you always required one then expect short shrift and possibly refusal of leniency. We have seen clients declined lending when a license should have been in place but wasn’t applied for until the mortgage application.
With a purchase most lenders will condition the mortgage offer with a grace period of 30-90 days.
Again if the council are known for delays then tell the broker who can discuss and clarify the lenders policy when this happens.