I'm nearly 4 years into my IVA.
I have started up my own business, funnily enough to sell insurance.  I got approved by the FSA to do this - I disclosed everything and they said my work experience was enough.  So I am directly authorised to provide financial advice.
Therefore I thought setting up a business bank account would be a breeze - I mean, if their regulator approves me, what's the problem.
In an attempt to be sensible and realistic, I applied in branch for NatWest's Foundation Business Account which is geared towards those with adverse credit.  After a laborious 1 hour meeting, all my details were sent away.  I received a flat declinature from their opening team within 48 hours with no reason.  When I appealed, they simply sent the usual "like all banks, we check credit reference agencies....etc" response.  Garbage.
I then went my current bank - Halifax.  They do not do business banking but their sister Lloyd's does.  Therefore I was referred to the business team.  I got an appointment in branch.  I was told that because I have been with them for over 3 years no credit check was required.  The business current account and savings account was opening there and then.
It amazes me the banking system in this country.  I would have preferred a careful assessment of my circumstances, which is what the banking regulator did with me.  Instead, one bank gave a flat "computer says no" and the other just signed me up with minimal fuss!
My advice - if you have been with the same bank for over 3 years, and they were not a creditor of the IVA, they should be your first port of call.