Firstly, you cannot go to prison for no licence/insurance/MoT, no matter how many times you commit the offences. So whatever it was your boyfriend was sent to prison for, it was not any of those offences.
How does he know that a bail warrant has been issued? The bail warrant means that he will be taken to the police station under arrest (if he does not hand himself in) and be formally bailed to appear in court as directed. If he fails to appear he will have committed a Bail Act offence and may be arrested and kept in custody until the next normal court sitting.
When he does eventually appear he will be well advised to produce medical evidence of his illness which prevented him attending court.
As far as sentencing goes, the criminal damage/tb offence should have no bearing upon the motoring offences unless he is either still subject to a conditional discharge or community penalty.
The sentence for No Insurance is a fine of one week�s income and between 6 and 8 penalty points or a disqualification. With previous convictions for No Insurance a ban is most likely. The licence and MoT offences will attract smaller fines.