I need advise if I could withdraw my tenancy agreement

- never received signed copy of the agreement (landlord never has time to sign it and the letting agent is still awaiting signature - it is nearly 3 months now)
That does not mean tenant agreement is invalid sadly. You accept you have signed it and you can request a copy under the Data Protection Act.
- I have reported that the flat has to under go some repairs such as boiler, broken toilet pump, mould issues (I have been told that I can do repairs myself and provide receipts but how can I do that if I have not received copy of the tenancy agreement?)
It does not make any difference, if you have received notification that you can carry out these repairs then you are able to do it and claim the money back. You do not need the physical agreement.
- I have informed letting agent about infestation as we have moths that are eating carpet and our clothing, he has arrange inspection with the landlord but landlord has never turn up and I end up with the letting agent asking me to wait for him to discuss issue with landlord.
You need to write to the agent and ask that unless the Landlord inspects and rectify the problem within 14 days otherwise you will sue for breach of contract.
Sadly you can't terminate the agreement based on this, if the property was flooded or not inhabitable then you could terminate the contract. But based on the above I am sorry to say that it would not be enough to terminate.
I am sorry if this is not the answer you are after and certainly not the one I want to give you, but I have a duty to be honest.
Can I clarify anything for you about this today please?
Alex