These are not all the same type of debt. The rent arrears and bank loan are entirely civil matters, & he could not be arrested in connection with them. However, he is wrong to say they will eventually be written off. It may be that the creditor will do this, but he can have no certainty about it. He is probably thinking of the limitation provisions, under which a creditor for a civil debt cannot take Court action to enforce the debt if 6 years have passed without payment or acknowledgment. However, this does not mean that the debt is written off - it still exists unless the creditor chooses to write it off. More importantly, this law does not apply if the creditor has obtained a Court judgement before the 6 years are up - which is what has happened to both these debts.
For Council Tax it is possible that an arrest warrant may have been issued, because imprisonment can occur for non-payment. I believe the same can happen for TV license, but am not certain. These things do not get automatically written off/cancelled after a set period but - as sara implies - it may be that they have effectively been "lost" because they were so long ago.
If he is in a position to make payments, the best thing would be for him to sort it all out.