Both HMP Oakwood, which is a super-sized jail holding up to 1,600 inmates near Wolverhampton, and HMP Thameside in London, are rated in the bottom category jails whose overall performance is of serious concern.
The third prison in this category is the state-run Winchester prison, which was criticised earlier this year for overcrowding and violence and where 10% of prisoners develop a drug problem.
The G4S-run HMP Oakwood was praised last year by the justice secretary, Chris Grayling, as a model for future prison development for its cost-per-prison place of £13,200, less than half the national average.
But both G4S and Serco came in for severe criticism from Grayling earlier this month for alleged overcharging totalling "tens of millions of pounds" on their tagging contracts to provide the electronic monitoring of curfew orders.
The annual ratings of prison and probation performance give a 1 to 4 rating based on 27 indicators for the 134 prisons in England and Wales, including the 14 privately run jails. One private prison, the G4S-managed Parc prison in south Wales, is among the 17 given a top rating for delivering exceptional performance.
The 35 probation trusts in England and Wales are all rated as good or exceptional in their performance despite facing abolition under plans now going through parliament to outsource 70% of probation work.
Frances Crook, of the Howard League for Penal Reform, said the ratings could provide no more damning indictment of the government's obsession with the privatisation of justice: "Last autumn, the justice secretary hailed G4S Oakwood as an example of what the private sector could achieve in prisons. We agree. The prison, ranked joint-bottom in the country, is wasting millions and creating ever more victims of crime."
Juliet Lyon of the Prison Reform Trust said the "good or excellent" ratings for the probation trusts should give ministers pause to reflect on their "ill-conceived" plans to hand most probation services to the private sector.