Normally, multiple entry visa are given to individuals who already received several single-entry visa beforehand. It is unlikely that you will receive one just after having one single, even unused single-entry visa in your passport.
In general, those visa are given only to reduce workload at the visa office, if it can be assumed that single visa for each entry would have been given anyhow. If there is no history of you successfully getting a visa, using it properly and leaving the country according to the terms, chances are low that you will get a multiple entry visa. This is why the Border agency recommends to apply for a multiple entry visa only after you have applied and used a single entry visa already.
The UK border agency lists the following points as consideration for long term (and therefore multiple entry) visa:
- whether you can show a frequent and sustained need to come to the UK (such as family links or an established business connection);
- whether your personal circumstances are likely to change significantly while the visa is valid - so you should give us as much evidence as possible that your circumstances will remain the same;
- whether you have shown that you can support yourself in the UK without public funds, and that you intend to leave the UK at the end of each visit; and
your previous travel history as shown in a current valid passport.
The first point is easiest proven with previous single-entry visa as mentioned above. The second point should be confirmed by providing your study documents so they know that you can remain as a student in the UK. The third point would be granted if you can provide a bank document showing that you have enough money to afford living the UK without the need for a job. Lastly, if you can show in your passport that you have frequently traveled to other developed countries and left them again according to the visa in the passport, your chances are even better.