OK, it looks like I confused "{32760}" and "{234565}"; however, I don't see "{234565}" anywhere in your code, although you state:

"... when I come to the part "RFC822.TEXT {234565}" I now need to read exactly 234565 from the string."

The string data you posted is multi-line (i.e. it contains newlines) so you'll need the 's' modifier if you want '.' to match newlines as well as other characters (see perlre: Modifiers). Here's a rough example of what I think you're looking for:

$ perl -wE 'my $x = qq{abcd\nefgh\nijkl}; say ">$x<"; say ">$1<" while
+ $x =~ /(.{3})/gs'
>abcd
efgh
ijkl<
>abc<
>d
e<
>fgh<
>
ij<
[download]

[Note how I've wrapped each string in angle brackets, so that you can see not just the start and end of each string, but also the placement of newlines within them.]

The caret (in your original code) still looks dubious. If it isn't, and you want to match the start of lines (in a multi-line string), you'll need the 'm' modifier (see perlre: Modifiers). Also, if you want to match the start of the entire string, use '\A' (see perlre: Assertions).