What can we do when the bank has told the landlord that we have to move out before the house can be put on the market?

That is ridiculous!  The lease is a binding contract and you can hold the landlord to it. Why would the bank tell the landlord that you have to leave? That does not wound right.  What else is going on?  First let's start with the lease: read it.  Does it have a termination clause?  I doubt it.  So the landlord can try and get you out voluntarily (which you do not want to do) or can evict you on the basis of some form of breach or for "cause" under the law.  Otherwise, the landlord is in breach.  I would speak with an attorney and discuss your options:  having them pay your moving expenses and a fee to finding a new place; staying put; whatever the law allows.  But do not be intimidated.  Good luck.

The bank is free to "say" anything it likes. However, if you have a signed lease that is good until May, then--so long as you comply with all terms (including certain unstated but implied terms) under the lease (pay rent, don't damage property, don't disturb other tenants, etc.), the landlord cannot make you leave until the lease is up. The lease is a contract, and it binds both parties.

Note that if you are "set up to move" in November, but the lease is until May, then unless the landlord agrees to let you move in November (if he does, get it in writing!), you could liable for rent from November to May (end of the lease).

The landlord is free to try to make it worth your while to move earlier, of course--he can offer you key money, pick up your costs to rent or stay in a hotel (and store belongings), etc. If it matters so much to him, see what he'll offer you.