Then I think you should write to BMI Baby asking for evidence that they notified you. If they cannot provide it, then I would go to small claims court. You can file a claim online, it is very easy and quick and low cost. You can recover your costs if you win. You do not have to go to the court, unless a hearing is required.
Here is a link which you can use to file the claim and get more information on the process.
https://www.moneyclaim.gov.uk/web/mcol/welcome
In general, I have found BMI Baby to be a bit better than the likes of Ryanair, so an initial letter outlining your claim and intention to pursue the matter in small claims, might be all it takes to get a resolution. Your claim should be for the following:
1. The hotel costs plus the cost of additional meals
2. The cost of the new airline tickets
Do not claim for the unused ticket to get you home, nor should you accept any payment from BMI baby for this amount.
Let us know how you get on...