Yes, most standard life insurance policies will provide instant cover for both natural and accidental causes of death as soon as your application is accepted.
The one exception to this is an over 50s plan which typically has a waiting period (or ‘qualifying period’) of 12 or 24 months, depending on the insurer.
Accidental death is often instantly covered from the moment you take out the policy, but natural death cover doesn’t start until after the waiting period.
In the event you were to pass away due to natural causes within this period, no lump sum pay out would be made, but all premiums paid would be refunded.