However my usual agent was not available due to uncontrollable circumstances.

There were three lessons learned. (1) Plan for unforeseen problems during the rehab.

Given this circumstances how can I provide any kind of objective evidence to negotiate asking price?

This may not work given the circumstances you described but I would ask the city zoning board if the property could be designated as a "nonconforming legal triplex" .

Due to unforeseen circumstances discovered by the lender, I as the buyer had to ask the sellers to extend our closing date to the following week from 11/15 to 11/22.

I have been blessed with a unique situation where someone in my family has given me the chance to inherit a property under the circumstances I repair it's damages myself (costs around £10k-20k) it is a 1 bedroom flat in west London and I've been looking to save for the repairs by working this year until march.

My insurance agent has suggested that I do a Homeowner Insurance Policy on the house, and require all the tenants to have their own renters insurance.It seems there are options (for instance, have a landlord policy on the house and renters policy on myself) so i'm curious, what has worked for people in similar circumstances in the past?

But I do use my inspection report to negotiate a lower sales price, if unforeseen problems are found.Case in point. 

(of course, you might need to sell a family home under special circumstances, that isn't what I'm referring to here!)

I guess it just depends on the person / price point & circumstances I suppose.