The time it takes to get your application approved can vary and the process is faster if overseas students apply for their visa outside the UK. UK Visas and Immigration (UKVI) say it can take them up to three weeks to decide whether or not to approve a visa if you apply for their standard processing outside the UK. Make your application inside the UK and it can take eight weeks. Wherever you apply you can pay extra for their priority service (https://www.gov.uk/faster-decision-visa-settlement), bringing decision times down to five days for priority and one day for super priority. However, these delivery dates aren't guaranteed even if you pay extra so bear this in mind when deciding which service to use.
There isn't a priority service option for the Graduate Route visa and this should be decided within eight weeks.