Yes, in many cases. If you have been paying full council tax without realising you were entitled to an SMI exemption or disability reduction, you may be able to claim a backdated refund. Some councils will backdate to the point when the disability began or when you first became eligible for a qualifying benefit.
There is no set time limit in law for how far back a council must go, but practice varies between local authorities. Some will refund several years without argument. Others may require more evidence. Either way, it is always worth asking, because the sums involved can be substantial.
You will need to provide your doctor’s certificate and evidence of qualifying benefit entitlement for the relevant period.