Verbal agreements

Tenancy Types and Management

Hi. We'd appreciate some advice on the following:
we have a situation where our tenants had agreed verbally to commit to 3 years in our property; in exchange we would drop the cost over the summer, and drop it by £55 pcm in the long term as well. It was worth it for the security of having these tenants for those 3 years.
We have had a few issues with them and with the property over the last few months: there has been rising damp (they were slow to notify us, so it was halfway up one wall before we saw it- we did deal with it right away though) and the bathroom suite (the toilet wasn't flushing properly, so our plumbers had a look and realised the whole pipe system needs re-setting). We have bent over backwards to accommodate them however, as they wanted to be in the house whenever any work was being done; to wait until after exams (they are married students) before additional work etc.
But today they gave notice, after just 2 years. We have replied by saying that they can get out of the contract if they pay us the money we have lost through agreeing to a deal that no longer stands due to their reneging on it.
Are we on solid ground with this? We have a signed tenancy agreement, but only a verbal contract as regards the 3 years.