Manhole you have opened looks rather clean to me to be foul or combined drainage, I suspect you may have separate systems, i.e. toilets, baths etc into the foul sewer, and rainwater into the storm drains. Run some water down the other (kitchen) gulley), does this back up or does it keep running away?
If this runs clear, then problem is likely in either the rainwater gulley, or system beyond it. Looks t me like an 'Osma' Bottle gulley. Remove the grating, you should see a 'shoulder' sticking out into the pot, in the top of the shoulder is a rubber plug. Carefully remove that, if water drains through the hole, problem is probably the pot is full of crud, clean out, replace plug and test with hosepipe.
If this runs clear, then problem is likely in either the rainwater gulley, or system beyond it. Looks t me like an 'Osma' Bottle gulley. Remove the grating, you should see a 'shoulder' sticking out into the pot, in the top of the shoulder is a rubber plug. Carefully remove that, if water drains through the hole, problem is probably the pot is full of crud, clean out, replace plug and test with hosepipe.