An in country application for FLR based on the IED (presume it is a WP) will be on a discretionary basis given you are now formally in the UK on visitor status - I presume you applied for a short period of leave to sort out your affairs/ perhaps attend graduation on form FLR(O) after completion of your studies. IMHO the IED FLR will be granted given your previous stay as a student in the UK. However this is not guaranteed and my concern here is that a refusal creates a negative record in your Home Office file.
However these (IED FLR) are taking a minimum of 5 weeks to get processed - depending on how soon the employer wants you to start then it may be best to apply for the relevant Entry Clearance at a
British Diplomatic Post overseas. This is usually granted on the day of application. Depending on your nationality it may be that the BDP has processing delays or may offer a restricted service e.g. some posts in the Middle East and the Sub Continent. If money is not an issue (travel back home then return to UK) and your BDP is offering a full service then its best to go home and apply for WP EC.
Note that a BDP EC is the only option if an 'in country' switch is refused - issue here is that the Entry Clearance Officer may want to dig into the reason for refusal which may hold things up as they cross reference with the HO. This can hold up your application for a while although it will be eventually approved.
Good Luck
