Note: this is VERY hacky. Perhaps there is a smarter way to do this. Anyway:
\documentclass[12pt]{report}
\usepackage[letterpaper]{geometry}
\geometry{verbose,tmargin=1.25in,bmargin=1.25in,
lmargin=1.4in,rmargin=1.15in}
\usepackage[doublespacing]{setspace}
\usepackage{indentfirst}
\usepackage{enumitem}
\makeatletter
\renewenvironment{thebibliography}[1]
{\chapter*{\bibname}%
\setbox2\hbox{\@biblabel{#1}}
\@mkboth{\MakeUppercase\bibname}{\MakeUppercase\bibname}%
\begin{enumerate}[itemindent=!,leftmargin=0pt,label={\@biblabel{\@arabic\c@enumiv}\setbox2\hbox{\@biblabel{\@arabic\c@enumiv}}\hspace{\labelwidth}\hspace{-\wd2}},labelwidth=\wd2]
\usecounter{enumiv}%
\sloppy
\clubpenalty4000
\@clubpenalty \clubpenalty
\widowpenalty4000%
\sfcode`\.\@m}
{\def\@noitemerr
{\@latex@warning{Empty `thebibliography' environment}}%
\end{enumerate}}
\makeatother
\begin{document}
Text goes here. ..\cite{ito92, joannopoulos95}
Here, n describes the increase in P1 by nucleation. The gain ($gP_{L-1}$) and loss ($-P_{L}$) terms are due to subunit addition.
\bibliographystyle{unsrt} \bibliography{references}
\begin{thebibliography}{11}
\bibitem{ito92}
Foo Bar Baz,
\emph{Lorem Ipsum dolor sit amet},
Consectetuer editions,
March 24th, 1993,
Rivendell.
\bibitem{mu}
qef
\bibitem{2424}
oihoiwrgh
\bibitem{qeqefqe}
3t31tsef
\bibitem{214}
qeeqfr
\bibitem{1235689}
12345678900987654321
\bibitem{3215}
asdsad
\bibitem{124124}
14124124
\bibitem{134134}
adgvadagd
\bibitem{foobarbazbellheisenbug}
Schrodinbug Heisenbug Schrodinbug Lorem ipsum dolor sit amet consectetuer adipiscing elit foobar
\end{thebibliography}
\end{document}
I redefined the bibliography environment to use an enumerate environment from enumitem, and fiddling with the parameters I managed to get the desired result. Many pieces of code are copied off the definition of the bibliography environment taken from report. My edits are in the part from \setbox1 to \usecounter. There, I set box 1 to \@biblabel{#1} which is the correct label width as was previously set by the class. \@mkboth is off the class. Then we have the list. THe options itemindent and leftmargin are set as suggested by "Original answer" here, so thank karlkoeller for that. label= is sorf of copied off the class, though the \hspace is what solved the problem in the comment's screenshot, or rather the variant where 1 was a bit to the right of the left margin: basically it places exactly enough space to align the 1 with the second line. labelwidth= takes the width of box 1 at the moment of the list's start (so box 1 is what was set by \setbox1) as its value. So the label width is, in this case, [10]'s width, but when the label would be tighter it is not flushed right but an \hspace is inserted that gets it exactly aligned on the left. Here is the output:

Is that it?
Simplified version still using enumitem
Change the code between \makeatletter and \makeatother with
\makeatletter
\newlength\biblabelwd
\renewenvironment{thebibliography}[1]
{\chapter*{\bibname}%
\@mkboth{\MakeUppercase\bibname}{\MakeUppercase\bibname}%
\settowidth\biblabelwd{\@biblabel{#1} }%
\begin{enumerate}[
itemindent=\biblabelwd,
leftmargin=0pt,
label={\makebox[\biblabelwd][l]{\@biblabel{\arabic{enumiv}}}},
labelwidth=0pt,
labelsep=0pt
]
\usecounter{enumiv}%
\sloppy
\clubpenalty4000
\@clubpenalty \clubpenalty
\widowpenalty4000%
\sfcode`\.\@m}
{\def\@noitemerr
{\@latex@warning{Empty `thebibliography' environment}}%
\end{enumerate}}
\makeatother
lipsumorblindtextfor filler text, and adding some kind of bibliography, instead of a lot of\includes which clearly cannot be of use. – MickG Oct 29 '15 at 17:31latexindent.plas themanual.pdfsays, would you :)? – MickG Oct 29 '15 at 17:48