Oh dear where do I start? I don't want to discourage you but there are some points which need raising. 1) Most refrigeration units have an overload device built into the motor as should the power be removed and then returned in a short time then the pressure will not have dropped before it tries to re-start and it would stall the motor. There are now some inverter models which don't have this, but other than those specials one has to be careful that there is enough power to start the unit most of the time or the overload will be tripping rather frequent and will fail. So most fridge/freezers state do not use with an extension lead. 2) A fuse has a resistance so if you have extension plugged into extension it's not only the wire which causes a volt drop but the extra fuse, so yes wiring a socket direct will help also the wire used to wire sockets tends to be thicker than that used for an extension lead. 3) There are three basic circuits used in the UK for sockets. a) The 32A ring final uses 2.5mm sq cable. b) The 32A radial uses 4mm sq cable. c) The 20A radial uses 2.5mm sq cable. You need to work out which system you have. With c) it's easy, with a) and b) you may need to fit a fused connection unit (FCU) there are rules which allow a unfused spur if followed, but you are not allowed to spur from an unfused spur. 4) Any new socket should be RCD protected and also any buried cable less than 50mm deep so may need a RCD socket or FCU with former may also need special cable if it is to comply. Old wiring does not need upgrading however. 5) The junction box you show needs the cables cleated so they can't pull out of the box and it has to be assessable so screws can be checked for tightness. There are maintenance free junction boxes with spring cable grips and cable grips built in which may be more suitable. 6) Before extending any cable one should test it to ensure the volt drop and loop impedance to ensure it will auto disconnect in the event of a fault is within the limits.
OK in real terms especially as a refrigeration unit look how close it is to the main incomer to the house. In my house all power starts at integral garage so no problem. If you intend to do DIY electrics buy a cheap plug in tester like the Martindale EZ150 these do a loop test which means it checks the volt drop and ability of the fuse/MCB/RCBO to disconnect in the time allowed, well near enough anyway electricians meters cost around £750 so can't expect a £50 plug in tester to be as good, but it is unlikely if it passes with the tester I have listed that there will be any problems. Clearly if this is the only DIY your intending to do then likely cheaper to get an electrician.
In theroy when a house has a new occupier it should have an electrical installation condition report (EICR) this should tell you earthing system TN-S, TN-C-S or TT and also the readings for loop impedance these reading should tell you if safe to extend or not.
With the ring final you could spur or extend the ring again the EICR reading will show if it can be extended or not.
The EICR can be expensive and often people have an unofficial one done where some electrician will have a quick look around and point out any problems which can be seen without making out a full report. If you don't have a report it may be a good idea to have first job done by an electrician and ask him if there are any blatant faults he can see.
If the wiring was not for a freezer I would not be so worried, but since the freezer is so easy damaged by volt drop in fact it is about the only house hold item which is damaged by volt drop, I have been careful to point out problems.
If we can help do please ask. You must remember on a forum others read your questions and can follow advice blindly so we do need to be careful. I do not want to put anyone off DIY but do want them to go into it eyes open.
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