I graduated with a 2nd lower so heres my opinion..
I feel that with a 2nd upper, you should do decently well in the
public sector although you will naturally lose out to the 1st class
or scholars who will waltz to the top assuming all things are equal
(ability, luck, etc etc)
I know you will want to compare upwards but do bear in mind that
there are many others who only have a 2nd lower and below who are
much worse off than you...
If you are planning for a career in the public sector why not
consider a masters in public policy from LKY school of public
policy where the minimum criteria is a 2nd upper?