Posted: 15/08/2013 at 16:04
The grass will thicken but I would be tempted to fork over the bare areas (which will help drainage), add sandy compost, some grass seed and then some more sandy compost to fill those areas out and keep watering the lawn. You have done well as seeded lawns can take a year or so to look good.
Cutting the lawn - I would wait till it it looks like it needs it, longer the better but certainly you can cut it before then end of this month if you use the highest mower setting.
If the water pooling continues then keep forking over the lawn and adding sandy compost afterwards to keep the lawn decompacted.