It depends on the site and the local authority. A single house on a rural site with good percolation often manages run-off entirely by infiltration, while a house connecting to a surface water sewer, or on poorly draining ground, may be required by planning condition to attenuate run-off and restrict the discharge rate.
Attenuation requirements come from two directions: building regulations require adequate surface water drainage, and planning authorities apply development plan SuDS policies through conditions on permissions. Where a condition specifies a maximum discharge rate, some form of storage is usually needed to achieve it.
The practical test is whether the ground can absorb the run-off. Where percolation testing shows good infiltration and there is space clear of foundations and percolation areas, a soakaway may be sufficient on its own. Where it cannot, attenuation with flow control is the standard alternative.