Cut-off time is configured in the eBay account:

1.In My eBay section click the Account tab and then click Site Preferences on the left.
2. Enable Same working day dispatch with order cut-off time.
3.Change the cut-off time for same working day dispatch to suit your business. The default time is 2pm - make sure you set an achievable cut-off time.

In Linnworks, to select same day dispatch, choose 0 Days from the Max dispatch time drop-down menu in eBay configurator > Shipping.