Bit of a conflict there it seems.... First step is to get a transcript of the judgement where a wasted costs order was made. If there's £30k at stake I really would instruct counsel to advise and draft the appeal. The 21 days is not an absolute bar, you just need permission beyond that and if you have good grounds and good reasons for delay its not generally overly problematic IME particularly if you didn't get a sealed order or transcript for some time through no fault of your own.
Have you already followed the firm's complaints procedure. If you do it is likely that they will agree to cover the costs if it was their omission that lead to adjournment etc. They will also let their insurer know of a possible claim.
There's a very high threshold to prove wasted costs. Higher than just negligence. You need to take that into consideration. Do you have an order for costs against you personally, or a wasted costs order?
The order against you won't be a wasted costs order, as they are made against legal represtantives. If you have incurred a loss because of your solicitor's act or omission then you may have a claim in negligence. I would contact your solicitors and complain in the first instance. You may be able to sort this out informally.
I second what Mumma said - it doesn't make sense that a wasted costs order would be made against you personally - the whole point is that they are orders made against your solicitor or barrister. Who is telling you you have personal liability for the wasted costs?
"The applicant shall pay the wasted costs of today..."
I really feel my lawyer should be liable for this
A claim for negligence seems a long process and I'll be chased for costs in the meantime and may have enforcement action taken against me which could have long term consequences like losing my job or not being able to get a loan/mortgage...
You should write to the barrister's head of chambers and complain. If they agree that the act or omission was the fault of the barrister I suspect they'll offer to recompense you (perhaps by refunding the fee you paid and also paying the costs order).
Presumably your barrister charged you more because you weren't able to present your case on a plate to him/her unlike the opposing barrister who was briefed by a solicitor.
There can be many reasons why one particular barrister costs more than another, including seniority and how many people want to book them.
Not much you can do other than pursue your complaint through chambers and see what you think about their response.
Your barrister cannot be responsible for errors made in the conduct of your case before they assumed responsibility. You must be very clear in what they were assuming responsibility for, as you are responsible for everything else.