At the meeting, held at the Ministry of Justice in Whitehall, the Winchester MP covered an 'improvement plan' they both expected to see following Her Majesty's Inspectorate of Prisons report into the Romsey Road jail.
The meeting with Mr Wright came after a recent meeting Steve held with Governor Dave Rogers, where they went through the report and discussed the addition of a Young Offenders' Institution to HMP Winchester.
Speaking afterwards, Steve said: "I was in with the Governor earlier this month to run through what is a hefty report full of recommendations and housekeeping points. I think it's easy to forget just how much change Winchester has faced in the past 12 months.
"The extension to becoming a YOI, now housing young adults with all the impact that has for relations among inmates, as well as taking up a great deal of regional slack as nearby facilities such as Reading are closed make it a very different place to the last Inspection report in 2012.
"There is clearly a lot of work to do still and investment needed but we have a stable senior management for the first time in many years and I very much used this report as the basis for my discussion with the Prisons Minister."