Then you are eligible to change status to F1 here in the US.
You cannot extend the internship. The regulations limit the duration and you have maxed out.
So if you want to go to school you have to apply, get accepted, prove to the international office you have the funds to live and pay tuition without working and they will then issue you an I-20. That is a form you have to send to USCIS with a request to change status to F1 student status.
You must file this I-539 before your J1 status expires.
Here is a step by step website that walks you through the process of becoming a student.
Instead of return to UK to apply for the student visa stamp you file the I-539 once you have the I-20 from the school
I am eager to make this a positive experience for you. Please ask follow-up questions if my answer is not clear.
I hope that I have provided excellent service and, if so, would love a 5 star rating. If not, please let me know how I can further assist you. In the future, you may begin your questions with “FOR JUDITH” and I will be your personal immigration expert.