Security firm G4S paid more than £415,000 to change the locks after the keys to a major prison went missing.
The incident happened weeks after the firm took over the running of Birmingham prison in October 2011.
The prison is one of four institutions which have had to have locks changed since 2010, the Ministry of Justice said.
Taxpayers' money was used to change locks at HMP Swaleside and the young offenders' institutions Glen Parva and Warren Hill.
The cost to the taxpayer of those incidents was £337,551 excluding VAT.
It cost G4S £415,276 excluding VAT to change the locks in Birmingham.
Mr Wright said: "None of the prisons were placed in lockdown following the incidents and there were no escapes at any of the prisons.
"Following these incidents vigilance at the prisons was increased regarding key security and events that may lead to a prison needing to be relocked."