My garden is completley waterlogged is drainage required?

[DOLL]

The garden is completely waterlogged and after digging down to do a soil test I have discovered it continues down for at least 3ft. A family member has told me that the whole garden will need to dug up at least 3ft to 4ft down and the soil removed and replaced, however he believes drainage is not required, surely the problem would just build up again? Any advice would be gratefully received.
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Drain survey