If you were to take the case to the small claims court, you would need to show your losses, normally a court will not award monies for stress and anxiety. Bear in mind that you are not guaranteed to be awarded the court fees even if you win the case – which would be £50 for a claim up to £300. And you won’t get paid for the time preparing your case and attending the case.
Had the move involved a property chain, there would likely be many possible knock on effects, at which a monetary value could be applied. But as you were moving to your parent’s home there would possibly be loss of access to the person who was moving into your home. They would need to make a claim against you for this, and you could then add this to your claim against the removal firm.
But if you are saying that you actually had no direct additional monetary costs as a result of the delayed move, only that you had to take a day off work for the move, I doubt the court would find in your favour for the following reasons:-
The court would view that you would have lost your personal time for the day of the move (let’s say it was a Saturday), but as the move did not take place you had most of that day to yourself.
Now you lost your time on the day the move took place (which happened to be a work day, for which you did not get paid). But let’s say you did not have most of the Saturday of the cancelled move to yourself, but went to work – then your losses would be negligible.
For this reason I think you would be lucky to have the court award you 100% of your lost wages for a day, because you had most of the original move day free. Although the removal firm’s t&c require you to pay 100% of the fee if cancelled within 24 hours – there is no such term requiring them to pay you if they cancel the move within 24 hours (or any other time period for that matter) – you cannot unilaterally change the contract, even if you think such a change would be fair.
So although I very much sympathise with the situation you were placed in due to the failure of the removal firm, your provable monetary loses are minimal, and even if you were to win a small claims case, it would be a pyrrhic victory given the time involved.