I have a court order stating that as a respondent for a Decree Nisi, to pay all the costs of the petitioner. I had offered to pay £750, when I was still working with a lawyer and when filling out the Notice of Proceedings I stated that "I did not agree that my behaviour was unreasonable but said I would not defend the case". I did not fill out box 6. The costs are around £4800, even though I have done nothing to defend my case. Is there anything I can do to appeal this decision? The order was made on the 9th of Jan 2020.
The divorce costs should be confined to the divorce process and not include anything to do with the finances.
If you weren't personally served with the petition, acknowledged it promptly and the divorce proceeded without issue, I would expect the costs to be £1200-£1800 depending upon which part of the UK you are in.
The order for costs usually says "costs to be assessed if not agreed". If so you can request that a detailed bill be delivered to you although this will increase the cost.
You should make an offer to settle to protect your position. If you have offered £750 this is unlikely to protect your position as you have been ordered to pay all of the divorce costs, not a reduced percentage.
The court fee alone is £550 so your offer only leaves £166.67 + VAT for the solicitors fees. For reference the solicitor's fee for the divorce should be around 4 hours at their hourly rate although the more expensive the firm the more people they have working on a case which adds to expense.
If the court has made the costs order, it has already decided that there is enough evidence of the unreasonable behaviour. Also, if you did not defend the petition (which is never a good idea anyway) you've not done anything to challenge the evidence.
As for appeal, you would first need permission to appeal before you would be allowed to apply to appeal. You would also need permission to appeal out of time as you need to apply within 21 days.
All of this is very expensive, is likely to fail, and you will end up paying more.
Is it possible though? Yes, it is possible. Personally though, I would run a mile - as soon as you start arguing about costs, the costs of those arguments begin to outweigh the original costs claimed.