Fixing a negative slope

Take grass out of the negative drainage area and put it to the side, making sure it is at least 6 to 10 feet from the house. Add at least 8 inches of new soil to raise the grade and this should force the water into the other direction.

Hard to answer correctly with out seeing the property and damp levels etc. But there mat be a way to re level the patio with the correct fall flowing away from the property ( as long as the finish height is not lower than the grass level) if so then a retaining wall will be needed. Also you can add a min 100mm void against the property wall and leave open of fill in with lose stones. But this all depends on damp course levels. 150mm below damp is a regulation but not always available. So then use the 100mm void . If its a smooth patio surface then aco drainage along the property wall. But if your lucky and can re level and raise the levels with out retaining then that's your best option.

Remove slabs and re screed from house on a decline towards end of patio 👍🏻

You can either lift and relay slabs or lay ACO drains on the negative slope to discharge water away

Install an Aco channel for the full length of the house and connect into existing soakaway or a storm drain.