As with any non inverter drive refrigeration unit volt drop is critical, the units have a compressor which should not be started under load, there will be times when it is started under load so it has an overload device to switch it off should this happen and give enough time for pressure to drop before it re-tries to start, these overloads are OK for the odd use, but if regularly tripped they will fail, so it is important there is not a volt drop over the permitted 5% and even the 5% could be a problem. The volt drop is important on start, once running not so much of a problem, and on start the compressor draws the maximum current so it must be considered as 13A. In fact it may be over 13A on start, even a fridge/freezer which uses less than ½ amp on run still uses 10A on start.
This is why nearly every refrigeration unit says you should not use an extension lead, one there is a volt drop on the cable and two a volt drop across the fuse so it would be easy to exceed the permitted volt drop, some plugs will take 2.5 mm² cable, but most you can't get over 1.5 mm² to fit, much depends on the volt drop already at the socket and for that matter the house, for years even though the official voltage is 230 volt many homes still had 240 volt, however with the role out of solar panels in order to stop them tripping out on over voltage the suppliers have started lowering the volts to the correct 230 volt, when it happened with my home the kitchen fluorescent lamp failed, was using a 58W tube in a 60W fitting, can't get away with it any more.
The way to test volt drop is to use a loop impedance meter, but that is not something the normal house holder will have, so all you can do is use the thickest cable you can and keep it as short as you can, not having two fuses would help, so getting a socket fitted near the drier will mean 2.5 mm² which will reduce volt drop and only one fuse so answer is to have a local socket fitted.
Yes there is a fire risk with extension leads, but that is not why it says don't use them, it is volt drop why. Any non inverter drive refrigeration unit says do not use extension leads, be it fridge, freezer, air con, or condenser drier all say do not use an extension lead.
Note:- Some fridge/freezers and freezers now use inverter drives, this means they use electronics and turn the supply to three phase and in doing so auto correct volt drop, so the new inverter units do not have the same problem, however manufacturers are proud of their inverter drives and will plaster it all over the appliance as a selling point, so unlikely your drier has an inverter drive.
