If you are studying at a UK university by distance learning, you are eligible to use the short term student route to visit the UK. Since you are a visa free national, you can apply for leave to enter the UK under this route at the border, each time you enter. In this case, your passport will be stamped with a short-term student stamp, which you should check before leaving the desk, since mistakes can happen. The criteria for the use of this route are:
An applicant who wishes to use short-term study to undertake distance learning in the UK must meet all of the following criteria. They must:
- be studying for the majority of their time outside of the UK for a UK qualification by distance learning
- be on a course that is longer than 6 months
- only enter the UK for limited periods, totalling no more than 56 days in the UK in any 6 month period - study completed during visits can include induction weeks, short periods of intensive face-to-face learning and exams or assessments
I believe that your university will need to confirm that your course is distance learning, perhaps in the form of a letter. It is not clear to me that a pattern of visiting two days every week is in keeping with intention of the route. You may contact the international office at your university to discuss this, but they might not be familiar with this entry route. In that case, you may need to engage your own immigration solicitor.
As with any visa free national, you could also apply for a visa (the short term study visa in this case) rather than seeking leave at the border, and this may be less stressful.
