You probably won't need to use any grass seed if you give it a good raking now, get rid of all that thatch, and then mow it regularly (at least weekly
) when it's growing. I can see you like a BBQ, and obviously spend some time fishing, but a weekly mow will and an occasional rake will sort that lawn out without spending a lot of money
Last year we took over a lawn which looked worse than yours, as much dead grass as you have plus lots of weeds, but having raked it hard one weekend (better than going to the gym) and convinced my other half of the necessity of a weekly mowing (I bribe him with bacon baps) has created a lovely green lawn (stilll with some clover in for the bees) for nothing more than the cost of a pack of bacon once a week 