Don't try this at home...
Mixing fonts in this way is not recommended and is likely to produce results which are significantly suboptimal.
However, if you really must:
\DeclareMathAlphabet\mathcal{OMS}{cmsy}{m}{n}
\SetMathAlphabet\mathcal{bold}{OMS}{cmsy}{b}{n}

Complete code:
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[polutonikogreek,british]{babel}
\usepackage{mathptmx}
\usepackage{substitutefont}
\substitutefont{LGR}{\rmdefault}{bodoni}
\DeclareMathAlphabet\mathcal{OMS}{cmsy}{m}{n}
\SetMathAlphabet\mathcal{bold}{OMS}{cmsy}{b}{n}
\begin{document}
This is English
\textgreek{Πάτερ ἡμῶν ὁ ἐν τοῖς οὐρανοῖς·}
$\mathcal{ABC}$
\end{document}
Based on egreg's answer to your earlier question. I can't find the code you are using for Times so I've guessed but it shouldn't matter.
[EDITED to simplify thanks to egreg's comment.]
\Declaremathfont
that I know of.... – cfr May 2 '15 at 3:23