Did you try the using "while", as well? I've got this:

#!/usr/bin/perl -w

my $string = '<a href="page.cfm?objectid=11933900&method=full&siteid=5
+0144"> Costly false alarms </a> <a href="page.cfm?objectid=11933890&m
+ethod=full&siteid=50144"> Mindless yobs terrorise OAPs </a> <a href="
+page.cfm?objectid=11933879&method=full&siteid=50144"> Road deaths </a
+> <a href="page.cfm?objectid=11933842&method=full&siteid=50144"> Twis
+ted porn pervert caged for life </a> <a href="page.cfm?objectid=11933
+800&method=full&siteid=50144"> Greenbelt homes plan appeal thrown out
+ </a>';

while ( $string =~ m!(<a[^>]*>)(.+?</a[^>]*>)!ig )
{
        print "1st match: $1 \n";
        print "2nd match: $2 \n\n";
}
[download]

and when I run it, I get this:

1st match: <a href="page.cfm?objectid=11933900&method=full&siteid=5014
+4">
2nd match:  Costly false alarms </a>

1st match: <a href="page.cfm?objectid=11933890&method=full&siteid=5014
+4">
2nd match:  Mindless yobs terrorise OAPs </a>

1st match: <a href="page.cfm?objectid=11933879&method=full&siteid=5014
+4">
2nd match:  Road deaths </a>

1st match: <a href="page.cfm?objectid=11933842&method=full&siteid=5014
+4">
2nd match:  Twisted porn pervert caged for life </a>

1st match: <a href="page.cfm?objectid=11933800&method=full&siteid=5014
+4">
2nd match:  Greenbelt homes plan appeal thrown out </a>
[download]

which I think is what you want. I first tried just doing a single "$string =~ m!(<a^>*>)(.+?</a^>*>)!ig" and then printing out $1, $2,...$8, and only got values for the first two. That "while" thing seems a little shady, for the reason I put in my updated post above, but it seems to work in this case.