Being in negative equity, in a way is a good thing, as they can't move you to a BTL product (which would carry higher rates and fees) as the LTV needs to be below sub 75%.
Consent To Let is given on a case by case basis. They will want to know why it's being let out, eg have you got to move to be closer to work etc etc? It will depend on things like, your account conduct, your credit score, your income and how long you've had the account.
What the lender is trying to suss out is if this is an attempt at a "back door BTL" Eg did you by the property a few months ago on a residential product (lower deposit, rates & fees) and now suddenly you want to let it out, this avoiding the higher deposit, fees and rates etc etc.