As soon as possible.
Liability
There is no contract here so you would be relying on the tort of negligence and/or trespass. If you have suffered damage from somebody else's negligence then they are liable for your loss.
Part of the problem that you face is you need to determine exactly who was potentially negligent.
It probably isn't your neighbour! It is quite likely that your neighbour was using a contractor; a contractor is not an agent and so your neighbour has not been negligent, the contractor has. If you were to sue your neighbour in those circumstances you would lose.
You need to take steps now to find out exactly who the person was who caused the damage - that's the person you would need to sue.
To win a negligence claim, you need to prove that the defendant:
- had a duty to the plaintiff,
- breached that duty by failing to conform to the required standard of conduct (generally the standard of a reasonable person),
- the negligent conduct was, in law, the cause of the harm to the plaintiff, and
- the plaintiff was, in fact, harmed or damaged.
If the facts are as you say:
- They probably have a duty,
- They probably failed in that duty,
- See below,
- You have clearly suffered harm or damage.
Types of loss or damage
The treatment of loss or damage under the law depends on what type of loss it is:
- Direct loss includes the repair and rehabilitation of the property - this would generally be recoverable, i.e. legally it is a cause of harm.
- Consequential loss includes the loss of rental income during the period that the property is unavailable. Alternatively, a court may consider that the loss is the cost of you providing alternative accommodation to the tenant if this was an obligation on you; this could be more or less than the rent. It would also include relocation costs etc. This is also generally recoverable.
- Pure economic loss would include loss of earnings if the tenant terminated the lease and you were unable to find a replacement or were forced to lower the rent as well as any advertising or agent's costs. While it is possible to recover this, it is quite likely that this would be considered unforeseeable and therefore not a legal cause of harm. The legal reasoning is that the loss (tenant terminating the lease) is too far removed from the proximate cause (damage to the unit) to hold the defendant responsible for it. You have already indicated that the tenant is trying to use the circumstances to their advantage; this is not something that could have been foreseen.
Duty to mitigate loss
You have a duty to mitigate the loss caused by the negligence. This would normally include ensuring that repairs were carried out in the most time and cost-efficient way possible. The defendant is only liable for reasonable costs; not actual costs.
Insurance
If a third party is liable for the loss, then they are liable for the loss irrespective of if it is covered by your insurance. Your insurance company can sue in your name to recover whatever they have lost; while they can, they will only if they believe it is commercially worthwhile.
You need to talk to your insurer to determine what they will cover and what they won't and if they are going to seek to recover and what they will do if you seek to recover - they may choose to take the lead and tack your stuff on the back.