The closures were made after the ICB carried out a review of its local services and decided minor injuries could be managed through self-care and facilities such as NHS 111 and pharmacies.
Patients were also told they may have to travel to their nearest urgent treatment centre in Kendal or Keswick, or A&E departments in Barrow or Lancaster.
But, after concerns were raised by residents a further clinical review was carried out.
The ICB said it would now make an exception for GP practices whose patients would have to travel more than “10 miles and 30 minutes” by car to reach an urgent care service.
“The ICB has ambitions to be an organisation that learns along the way and to do this, it recognises it is necessary to listen to local communities to ensure the right healthcare systems are in place,” a spokesperson said.