You were actually on exactly the right track with your first regex. The simple trick is to assign $1 to another var, modify that var, and then use the modified value as the substiution like this:

$html =~ s/\n/<br>\n/g;  # assume this, and then fix <br> in pre block
+s with.....

$html =~ s{<pre>(.*?)</pre>}
          { local $_=$1; s/<br>//g; $_ }gse;

print $html;
[download]

We need the /g of course, the /s to make . match \n if present and the /e to exec the code in the replace block. The last thing evaluated in the replace block is what is used.