Hello again - I had to dash off the previous post so this is a bit more considered !
The situation described is a bit unusual. The professionals should notify their professional indemnity insurers who will decide two issues. Firstly, are they providing indemnity to their policyholders ? Secondly, if they are indemnifying their policyholders, they will carry out investigations to determine if they they going to contest or settle your claim.
I would always be worried about professional indemnity insurers not covering their policyholders. In simple terms, the insurers are the finance behind the surveyor and the engineer. So, unless the defendants have substantial means there would be no practical purpose in suing them if they cannot meet any judgment for damages and costs. The proofs for a professional indemnity case are usually onerous and would include getting other surveyors and engineers to opine on the errors or omissions of the first pair never mind the costs of putting the defective structures right (or the depreciation of the value of the property if that measure is to be used to assess quantum). You will also have a fairly hefty legal bill by the end of the process.
As mentioned above, if you serve proceedings on the defendants you can get a default judgment against them if they fail to respond to the proceedings. The convention is that if defendants fail to respond to legal proceedings they are effectively deemed to admit liability. If you get such a judgment the case will eventually proceed to a hearing to assess damages. The problem is that if the insurers are not involved you will be awarded damages and probably costs against impecunious defendants. One serious problem there is that the legal bill is actually yours to discharge to your solicitors if the other side do not pay. There are some side issues on this point but we don't need to go there presently

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You asked about suing the insurers. The parties against whom your rights of action lie are the engineer and the surveyor. I think in this type of case that you would have no direct right of action against the insurers as you have no contractual relationship with them. There could well be a different answer to this point if the proposed defendants were bankrupt as individuals or wound up if a company. I think that this latter scenario is still covered by S.62. Civil Liability Act 1961 but again you really do not want to be trekking to that particularly exotic part of the legal jungle just yet. Link for info
http://www.irishstatutebook.ie/eli/1961/act/41/section/62/enacted/en/html#sec62
In short, it does not cost much to serve proceedings as a preliminary procedural step to put the skids under the defendants to show that you mean business. However, you need to be very wary about going the full distance if there is nobody to pick up the bill.
Incidentally, you should have obtained an estimate from your solicitor about the likely costs involved in dealing with this matter. They are obliged to give you an estimate for the likely cost of the work - what is known as a Section 68 letter. Link
http://www.irishstatutebook.ie/eli/1994/act/27/section/68/enacted/en/html
Be careful out there - it really is a jungle. Good luck....