Unfortunately, proof of postage does not infer proof of payment in law. If your car is parked on the road without an appropriate tax disc, it can be clamped, towed, and eventually crushed if not claimed and taxed correctly.
If the clampers have put an appropriate notice on your car - and I am sure they will have - confirming who has clamped it and why, then yes, it is illegal to remove the clamp, and will simply add to your legal and financial woes.
Sorry to be the bearer of bad news, hope you get it sorted.