I can't second guess what a bank might decide but I think you need to rethink how you approach the question. Firstly, the banks have to be pro-active in dealing with arrears, collective can-kicking has not done the banks, or borrowers in arrears or the country as a whole any favours. They aren't asking for a statement because they want to personally catch you out. They are asking for a statement because they need to try and deal early with problems before they become catastrophic. On the whole it is a good thing, even if it is uncomfortable. Secondly, has the gambling contributed to the problem? In other words, if you hadn't gambled would you have been able to handle the unexpected bills? It is probably fair to guess that it has contributed to the problem but that doesn't mean that the problem wouldn't have arisen anyway. Sometimes big bills come up and we don't always have the immediate means to handle them (this is of course where savings come in, I'm guessing you have no cushion there). Thirdly, if you have truly "knocked it on the head" then that will also show in your statements. Perhaps as an additional step seek support, an ounce of prevention is better than a pound of cure. Even if the gambling hasn't become problematic or addictive yet, better to deal with it before it does. And it would demonstrate that you are taking the issue seriously and acting to resolve it and ensure it doesn't happen again. You need to be pro-active too. Another thing to consider is whether the bank actually has any incentive to force a sale at this point. Leaving aside the fact that selling costs money, if you are in negative equity, forcing a sale would be counter-productive, they would still need to arrange with you for the outstanding balance. Even if you are not in negative equity they will get more money from continuing the mortgage because of the interest you pay. Basically it may not be in their best interests at all to force a sale.
Fill in the statement anyway (even if you refuse to share it with them) and look honestly at what it is telling you. Can you afford the mortgage? How can you reasonably tackle the arrears? How can you plan to prevent a recurrence? Once you have all that in front of you then you will be better placed to argue your case with the bank.