Your scarification will have “opened up” the lawn allowing the new grass seeds to germinate. The top dressing gives a perfect seedbed for germination.
You should overseed with a grass mix reflecting the direction you wish to take your lawn.
For example, you could overseed with a drought tolerant grass, a fine grass or maybe just a modern, disease resistant general hard wearing grass seed mix. Remember, you get a free pack of grass seed when you buy Top Dressing from TurfandStuff
There is much debate about what rate you should overseed at. Apply a rate of about ½ of the normal sowing rate but if you have heavily scarified or are late in the season, slightly more can be applied to compensate.
The seed should be applied by mechanical Lawn Spreader and not by hand, as re- spreading later is very difficult.