Although this website is about transferring universities, it is also common for students wishing to change course within their current university.
Generally there are two times you can request to transfer course without having to restart the year, this is at the beginning and end of the academic year.
When trying to transfer at the beginning of the year the exact timeframe of when you can request will vary from university to university. The ease of which this can be done will also vary depending on where you are studying. Some universities will promote this and actively encourage it, while offers will only accept if the student makes a worthwhile case.
As with most things within education, your previous results (such as A-levels) will be a major factor of whether the university approves or not, although at times passing an informal interview would suffice.
If trying to transfer at the end of the year, then this is much easier and the majority will allow you to move courses as long as you meet the requirements for the modules.
As always, we would always recommend talking with someone within your university, they will be best placed to give specific advice and information on what you are looking to do.