Students on an undergraduate Medical, Dental, or Veterinary programme, either at King’s or another institution, can undertake an intercalated degree during their studies.
Whether you're intercalated degree is at King's or at another Student sponsor, as long as you have enough immigration permission to undertake the intercalation, you don't need to submit a new Student visa application before you start the intercalation.
If you need further leave to intercalate (at the same or a different sponsor) or to complete your course (having completed a period of intercalation), this will be considered as academic progression and you'll be able to extend your Student Visa from within the UK.
If you have further questions about this, please contact Visa & International Advice.