You can start a Ltd Company and it's finances would be it's own. However the books would be scrutinised by your IP and you would only be allowed to re-invest a nominal amount of "working capital". You will not be allowed to squirrel away money in the company coffers while you draw a meagre dividend, so, in the same way as if you were a sole trader, profits would still go toward the IVA payment.
If you get an off the shelf company the Articles will, most likely, prohibit directors being in debt solutions, but this can easily be remedied by a resolution.
If the company needs credit you, as a director could be credit checked, which will fail, or you could be asked to give a personal guarantee, which you cannot do -- so no credit facilities.
As you rightly say, a bank account could be problematic, but not impossible.
My opinions are merely that .. opinions based on experience. Always seek professional advice.
IVA Completed 23rd July 2013 .... C.C. 10th January 2014