Thanks for the feedback everyone. I appreciate the clarification as to what constitutes a reasonable cost (i.e. all letting agent costs associated with re-letting the place + the rent owed for the remaining months of the contract). I spoke with my letting agent who agreed to waive the check-out fee for me and the landlord, which took a bit of the sting out of the costs. I’ve paid the fee and already have viewings booked for potential new tenants.
Going to switch notifications off on this post now but I hope anyone who stumbles across it finds it useful!