The damages that can be claimed from breach of contract are those which " naturally flow from the breach" Whilst this sounds promising it is not as liberal as it sounds. Unlike the USA we do not have punitive damages in the UK. This means that any compensation must be tied in to a specific financial loss.
As such if you can point to specific financial loss caused by the breach that is not covered by the amount paid you can claim for it.
Having said we do not award punitive damages you can claim damages for distress and inconvenience but this award is very low usually a few hundred at most.
It may well be worth a letter of claim but I would not litigate on this.
I hope this helps, albeit in a negative way. If there are any further points please reply I will be happy to respond .