If the IAS reject your appeal, so what? Their decision is not binding on you and you certainly don't pay.
You will have to now weather the useless debt recovery letters. Debt collectors are powerless to do anything except to try and intimidate the low-hanging fruit on the gullible tree to pay up out of ignorance and fear.
You come back when you receive a Letter of Claim (LoC) and we take it from there. Depending on which bulk litigator NPC use, a suitable response is provided and then you wait for the actual N1SDT Claim Form. Again, we advise on how to defend it and provide a suitable template defence.
Eventually, the claim is most likely to be struck out or discontinued. Of the very few that ever go as far as an actual hearing, most those are won. Nothing we advise on risks a CCJ.
That appeal decision is exactly as predicted. The IAS is a Kangaroo court and, as you can see by the waffle the feckwiot who penned it, is not really a solicitor and certainly not a barrister either. A Barista, maybe. You certainly don't pay the scammers.
I have already given you the advice that you need to follow. come back when you receive a Letter of Claim (LoC).
Thank you for your reply
Is there any chance that they will accept an offer of £20 as an admin fee to finish everything so I can save the time ?
Possibly, but by doing so you are admitting liability and they are more likely to pursue you even more aggressively for the full amount. Your choice.