It's a B&S engine, Castlegarden body, 18 months old.
Was using it last night and whilst it eventually started on each occasion, it often took a lot of very firm pulls of the cord to get going.
Also, I could hear a little 'popping' sound sometimes when the engine eventually started to tick over. My not very well educated guess is that this sound may indicate that the spark is getting weak.
Could be the air filter? This can become dirty, you can try removing it and see if the performance improves. If it does then clean it, leave to dry and put it back in or replace with a new one. Over priming can cause this to become dirty. I think B&S recommend that you should push the prime "pump" no more than 3 times.
On mine it is enclosed by a square shaped plastic cover close to the primer pump. It's held in place with just a single screw. Wouldn't recommend using the lawnmower too long without it but at least you can see if the performance improves.