Patrick Kelly and Feilim O'Hadhmaill are protesting against being ordered to do prison work and being separated from relatives by glass security windows during visits. Their association with other prisoners and phone calls to relatives are also being restricted.
The dispute could add to the tensions already surrounding the Ulster peace process.
Kelly, 42, from Ballybrittas, County Laois, in the Irish Republic, was jailed for 25 years in 1993. He was intercepted as he drove a huge lorry bomb into London, and shot and wounded a police officer during the ensuing chase.
O'Hadhmaill, 36, a former sociology lecturer, from Accrington, Lancashire, also received a 25-year sentence at the Old Bailey last year. He was convicted of conspiracy to cause explosions.
The two men were transferred to Whitemoor from Full Sutton prison, Humberside, last Tuesday as part of plans to reduce the number of Irish republican prisoners held at the latter jail. When they refused to do the work, they were placed in solitary confinement.
These regulations are being strictly enforced because Whitemoor was the scene of an armed breakout by IRA prisoners last year and was subsequently the subject of a highly critical report on security.Reuse content