Please see the scope of registration for the regulated activity of Personal Care on the CQC website here . Here you will see that to fall into scope for this regulated activity the care must be provided in the place where the person in receipt of care is living at the time. Therefore of care is only provided outside of their home it would not require CQC registration.
In terms of the administration of an epi-pen, this would be the same, however, if the epi-pen is administered by a listed healthcare professional this could then fall into scope for the regulated activity of Treatment of Disease, Disorder or Injury here.