Sorry to hear of the issue.
Whether your limited company is liable depends who the plumber had the contract with.
I appreciate the investor funded the work but it comes down to privity of contract and who that contract is with. If you commissioned the plumber then it's liable your company contracted with the plumber which is why they are demanding the money from you.
You could refuse on the basis the work was poor and on that basis they are in breach of contract.
They should send a letter before action to you if their debt collection attempts fail - which is required under the pre action protocol to give you the chance to avoid court action. They usually give you 14 days to pay before they will take civil court action.
It is recommended that you reply to this letter given the courts expect parties in a dispute to engage and discuss their dispute, to try and avoid court action.
If they do sue, you will receive court documents (a response pack) which you must complete and return to the court. It is a tick box exercise for the most part and there is a short section to write a defence which is easy enough though please feel free to come back to this site if you need any more help.
You should not ignore the court papers as if you do, the claimant will apply for judgment in default meaning they win and you would not be allowed to defend the claim.
A claim will also take 9-12 months to be decided at court. If you lost then you would get 14 days to pay the judgment before the claimant can enforce the order, and 30 days to pay in full before it is registered with credit agencies. The claimant cannot recover legal costs if they win, in a claim under £10K (a small claim), all they can claim are the court fees and interest.
If the claim has no merit (e.g. the contract was not between the plumber and your limited company, or if they don't deserve payment because the work was sub standard) then you have an option (after your defence is filed) to apply to strike the claim out. The court will consider an application if the claim has no merit, or is misconceived.
You should first invite the claimant to voluntarily discontinue their claim within 7 days if it gets to this point - tell them if they don't then you will apply to strike out and seek your costs if you are forced to do so. If you have no response or they reply and refuse then you could apply to strike out. The application costs £275 but this is recoverable if your application succeeds. If you won the application, the claim is struck out.
The hearing (if the case gets that far) is likely to be held remotely, it's you, a district judge (who is a practising solicitor or barrister) and someone from the claimant company. The Judge decides and if you lost, you get 14 days to pay the sum. If paid in full within 30 days then nothing goes on your credit record.
If required I can assist you going forwards if it gets to the point they issue a claim.