You shouldn't have left with taking legal advice or reaching an agreement with the landlord - in most cases you will be liable for the whole term of a business lease.
You should take legal advice immediately. The key question is: Was the property in such bad condition that the landlord could be considered to be in serious breach of his responsibilities.
For this to be the case, the property would have to be unsafe, unusable, or non-compliant with legal standards.
From the information you've given, it's unlikely the electricity issue would meet that bar. You signed a lease knowing there was no live supply; should have checked all this beforehand, along with confirming who would be responsible for getting the new meter fitted.
Why are you still without electricity after a month though? You mentioned not wanting to pay for an engineer to come out, but it comes down to who the contract holds responsible. If it's you, not wanting to pay for an engineer would not be grounds to break your contract. If your landlord is responsible, it might meet the bar for your property being unusable.
With the key, are you saying that your property is currently completely unlocked 27/7 and accessable to anyone with access to the main building (which is presumably open to the public during business hours)? That may invalidate your insurance, and meet the bar for unsafe/unusable.
You can sue for losses if you are successful in breaking your contract due to your landlord being in serious breach. You're unlikely to get anything for the furnishings though as you still have them, unless they are some kind of bespoke item that would be impossible to use elsewhere.