Start at the beginning, what is the garage consumer unit fed from, there is no point fitting any extra MCB's or up grading if it has not got the supply to start with, old house my garage was fed from a 13A fuse in a FCU from the house ring final.
Next we come to if you can up rate anyway we are looking for the loop impedance, you should have some paperwork for the garage installation, however should does not mean it always exists.
What we want is if there is a problem the protective device will trip in the allotted time. So a 16A type C should trip at 10 times the rated 16A with a short circuit using the magnetic part of the trip, so 160 amp, and we allow for 5% safety margin so 168 amp. 230/168 = 1.369 ohms, so we are looking for an earth loop impedance of 1.37 ohms.
The problem is the cheap plug in testers like the Martindale EZ165 show the circuit is better than 1.7 Ω so can only test a 25A type B, I have always felt it is a bit useless when the standard British ring final needs 1.37 ohms as well, but it seems they are designed for the European system not ours in spite of having a 13A plug built in.
So cheapest tester I have found around £125 where simple plug type around the £50 mark, as to if with RCD protection you really need the magnetic part of the MCB to work is open for debate.
In the house it is unlikely that the supply is going to have an earth loop impedance over 1.37 Ω but in a garage it depends on the garage supply. If you already have a B32 for the ring circuits then it should be OK as the magnetic part of a B32 trips at the same current as a C16.
You can ignore the rules, but then what was the point in asking the question? I will be frank my loop impedance tester has failed so I can only use my low ohm meter, they have to use at least 250 mA so not a multi-meter, and I have not tested this house, I have simply taken the readings on the installation certificate and gone by them.
As to replacing a 13A socket with a 16A socket you would need something like this
So there is a provision to fit a MCB if feed from a standard ring final, but this
if fed from a 16A supply as 16 amp plugs have not got a fuse in the plug, so it is common to have a dedicated supply for a 16 amp socket as that's the cheapest method.
Personally I would try first with a 13A plug, and suck and an see, I have fitted a 16A socket to supply a caravan in the past, but it was supplied from a fused connection unit with a 13A fuse. It was only really to keep the battery charged.
