Tweeting ministers does absolutely nothing. I doubt they even count the tweets.
You need to either write to your own MP making your points and asking for them to by raise with the Justice Minister (sometimes MPs needs asking more than once to do this - mine does) and you should then eventually receive a copy of the response by the MOJ. Meaning the MOJ have to actually formulate a response which will stir their lazy bones into looking at the situation. Tweets they can ignore.
The other option is to right to the Minster of Justice directly at the ministry making clear that you are writing to minister (not the MP). MPs are not supposed to get into correspondence with other MPs constituents. But they can respond as minster from the ministerial address and sometimes will do so. If you writer to the minister at the HofC not the ministry you'll get ignored.
Anyone wanting to write to his or her MP can get loads of useful details from Sex Matters including a clear break down of the issues with a downloadable copy of the document produced by this staff group.
Excellent summary piece by Sex Matters which has lots of details if anyone wants to take this to their MP
sex-matters.org/posts/updates/mass-harassment-in-hm-prisons-and-probation-service/
I can't write to my MP as I have just written about something else (and too many letters starts to make you look like a nutter). If anyone does write and gets a MoJ response it would great if you didn't mind sharing it with us!