Can I seed over an existing lawn?

BML

I had a lawn laid last Autumn and the incessant rain helped it establish itself.  The sun shone last week I cut it for the first time.  It was only when I dumped the grass cuttings into the bag half full with the cuttings from the other lawn that I noticed that the grass blades from the new lawn are at least twice as wide as those on the existing lawn.  Actually it doesn't look to bad but can one change the character of a lawn by chucking finer grass seed over what I would call, "rough" grass?    

Allotment Boy

The rough grass you describe is probably a rye grass which will tend to dominate but most lawn mixes are just that, a mixture of various grass species to acheive a balanced lawn. You can overseed a lawn to help thicken it up, but you are not going to be able to go from a utility grade to a fine bowling green grade by over seeding. So long as that is not your aim do give it a go I am sure you can get a better lawn than you say you have now. The RHS website and a company called Lawnsmith have lots of on line advice.
  www.rhs.org.uk/advice/profile?PID=514
www.lawnsmith.co.uk 

BML

Many thanks for all of the advice.  Now to carry it out.