I agree it would be good to have fewer foreign prisoners in our jails.They are expensive and have in recent years added to the overcrowding.
The first thing government needs to do to cut numbers is to get proper control of our borders. Stopping the current big flow of new arrivals would stop the expansion of migrants and so reduce numbers which include some future criminals. Better border control backed by intelligence could also do a better job stopping people with a criminal record coming here.
The government says it now plans to send people found guilty of a crime back to their home country. As Robert Jenrick has pointed out their home country might not want them .The UK should withdraw aid money and visas from any country not cooperating with returns.
That leaves the issue of what if the receiving country lets them off any time in prison? The government should get agreement from the main countries involved that where a returnee is guilty of something that’s a crime in their country as well there will be punishment.
There also needs to be better border checks to ensure no criminal sent abroad is given entry to the UK if they return.None of this is possible without much better records of who comes in how long, with proper follow up when visas expire.