Mechanism for Chromyl Chloride Formation
The answer may (and does) lie in the oxidation potential of the halogens. As we move down the group 17 the tendency for oxidation increases.

Refer:
$$\ce{H2SO4 + HBr -&gt; Br2 + SO2} \tag{unbalanced}$$
but
$$\ce{H2SO4 + HCl -&gt; X} \tag{does not occur}$$

$\ce{K2Cr2O7}$ is not able to oxidise $\ce{Cl-}$ to $\ce{Cl2}$ but it does so with $\ce{Br2}$, thus we observe reddish brown fumes of $\ce{Br2}$ as if $\ce{Br-}$ had been present, which are then passed through $\ce{NaOH}$ to confirm the presence of chloride or bromide.

Refer:

\begin{align*}
\ce{CrO2Cl2 + NaOH -&gt;&amp; Na2CrO4} \tag{yellow soln,unbalanced} \\
\ce{above + H+ -&gt;&amp; (Cr2O7)2-} \tag{orange solution} \\
\ce{Br2 + NaOH -&gt;&amp; NaBr + NaBrO3} \tag{light yellow soln}
\end{align*}