If you are currently studying or have previously studied in the UK using a Tier 4 (General) or Student visa and you need to apply to extend your stay in the in UK (apply to extend your visa in the UK), your next programme of study must demonstrate 'academic progression' from your last.
The academic progression requirements
The Tier 4 Policy Guidance states that in order to demonstrate academic progression:
a) you must have successfully completed the course for which your most recent visa was issued; and
b) your next course must "normally be above the level of the previous course for which you were given Tier 4 leave". For example if you have previously studied or at Bachelor's degree level, your next programme should normally be at least at Master's degree level.
If you cannot demonstrate academic progression you will not be eligible to apply to extend your visa in the UK, although there are some exceptions to this which are explained below.
If none of the exceptions below apply to you, you must leave the UK and apply for a new visa from your home country. There are no academic progression requirements for applications submitted outside the UK.
You will be exempt from demonstrating academic progression (and can apply to extend your visa in the UK) in the following circumstances:
Studying on a new course at the same academic level as your previous course
In this case, the University must confirm on your CAS that: "the new course is related to the previous course for which you were given Tier 4 leave (meaning that it is either connected to the previous course, part of the same subject group or involves deeper specialisation); or "your previous and new course combined, support your career aspirations"
Continuing study on the same course (PhD only)
If you are granted a concession allowing you more time to complete your PhD, you can apply to extend your visa in the UK.
Please note: It is not possible to apply to extend your visa in the UK if extending or repeating part of a Bachelor's or Master's degree.
Adding a work placement or study abroad to your course
If you are adding a work placement or year of study abroad to your course, you can apply to extend your visa in the UK after the placement or study abroad has ended.
If you are applying to study a new programme in the UK and have previously studied in the UK using a Student or Tier 4 (General) Student visa, the new programme must represent academic progress from your previous study.
If you do not meet the academic progression requirements and none of the exemptions above apply to you, you cannot apply to extend your visa in the UK and must apply for a new Tier 4 visa from outside the UK
This and further explantion is available in the Tier 4 Policy Guidance