If compensation was awarded as a result of a criminal conviction (I assume this was a case of criminal damage judging from your first question) then the court decides how it (along with any fines, prosecution costs and victim surcharge) will be paid. Where the defendant is in receipt of benefits the most that a court can order is for the sum to be paid at the rate of £5 per week. This can be collected directly from benefits but, as hc correctly points out, this can only be done by agreement and it cannot be done where certain benefits are being paid (though straightforward "Job Seekers" allowance is not a problem. Otherwise the defendant is responsible for making the payments at the agreed rate. When payments are made compensation takes priority over any other charges.
You do not have the authority to instruct bailiffs to collect the debt as technically it is owed to the court, not to you. However, at the time of sentencing the court should have made a “collection order”. This means that if payments are not made as ordered then action can be taken to recover the sum without the matter being returned to court.
In short it is up to the court to collect your compensation and their process will follow up the matter if payments are not made as ordered.