Call them, you do not know who else may be reading this. You knew the battery had value, they did not. Your net return on the £3400 claim is £3920. How long do you think it would take to trace the details on Halfords/Wheelies records and follow it up?
A delayed disclosure will not go against you. Remember if the stuff hits the fan it's the whole claim they will go for not just the surplus. Believe me being grilled by a retired Army Redcap turned insurance investigator with a file of carefully prepared papers will make your 'what battery' comment stick in your throat as he explains exactly which one. Your whole financial set up can be inspected. As my old boss used to say 'Nae one's a clean tattie ' Over claims are costing others higher premiums. One of them might just decide to stick you in.
The situation would be no different if you found the bike in a hedge, you could not just keep it ,it is the property of B&B. How you interpret what you were told is irrelevant, you have a legally bound duty to take all reasonable steps to mitigate a claim. Insurance contracts are drawn up on the basis of good faith. The staff have probably no idea what a battery is worth. Yet. The risk is some smart young lad looking for promotion brownie points will pick up on it and get a nice recovery on file at his next performance review.
What you should have done- Asked what to do about the battery, in writing, pointing out that as a special and deteriorating item it has little value, offer £20 they would probably have accepted.
What to do now is up to you. Read the above sentence carefully . I have no further interest in this. Again tell me if I'm wrong.