I’m living in Riverchapel and our back garden garden have a layer of surface water that stays for days at a time if it rains. We only get sunlight to the very back of our garden which helps with drying it off also the grass is very patchy. It is a 2 year old house and we have no experience of gardening so haven’t a clue what is could be or where to start resolving it.
Usually an outlet is impossible because it would flood neighbouring gardens. But you could try a soakaway, which is a pit dug in your garden to get water down from the surface.
The problem is probably due to compaction and this is usually a layer below the surface and often it can be breached to allow water to drain away, by making a narrow hole and filling it with stone to within 15cm of the surface and then soil with some coarse sand mixed in. Or dig out a bigger soak-pit.
More on this at: https://gardenie.wpengine.com/gerrycategory/drainage/?id=5414