Thanks for the pics. We like pictures
The thing that is tripping is an RCD, which detects earth leakages and trips off. It is very sensitive, and does this before they get big enough, or last long enough, to be dangerous. BTW the RCD is not the
culprit; it is detecting a fault elsewhere and switching off the power, which is its correct function - it is a safety device.
I see you have a very good quality Consumer Unit, although I see from the colour of the printing and the test label that it is about 10 years old. It is likely to still be in good condition, though. However I notice that it has "C" type MCBs fitted, which (although they fit) are an Industrial device - it may have been fitted by someone moonlighting on domestic work or using second-hand parts. In particular, the use of C10 for lighting circuits is likely to be incorrect in a domestic installation and would need to be justified by a design calculation which I suspect may not have been done. The MCBs can be swapped for a few pounds each. But this is not relevant to your presenting problem, so we will put it aside for the moment.
Q. Do you want to try to fix this yourself, or would you rather get an electrician in?
I think that probably you have some earth leakage on your cooker. This may be for example the oven element insulation breaking down with age (this is very common and not usually dangerous), or it may (less usually) be damp getting to something, perhaps as a result of cooking spillages, or a cable being damaged, for example by mice or having a heavy object on it.
IF this is the case, there are two ways of dealing with it (1) have the cooker fixed (2) move the Cooker circuit to the RHS of your consumer unit (3) do both these things (best option). The circuits marked in Green are protected by the RCD, this provides an additional layer of safety for appliances that might be used outside or in damp conditions (including kettles and showers or other appliances that may get wet in use). the circuits in Red are not RCD protected, and this is usual for circuits which are not portable and likely to get wet. This includes lights and (usually) cookers. An electrician could move the circuit inside the consumer unit very easily.
A few easy tests you can try that will give us more information:
(Test 1) If the MCB (switch-like thing in the consumer unit marked "C32" and labelled "Cooker") is switched off (so the cooker circuit should seem dead) but the cooker control switch on the wall in the kitchen is "on" and the cooker knobs (including oven and rings) are "On"; does the RCD still trip?
(Test 2) If the MCB is "On" and the cooker switch on the wall is "off" and the cooker knobs are all on, does it trip?
(Test 3) If the MCB and the Cooker Wall switch are on, but all the cooker knobs are set to "off" does the RCD still trip?
(also, as Davy says, above - look for any signs of damage or loose wiring.
And tell us if there have recently been any alterations or events that might affect the wiring - including nails into walls or floor; mice; puppies; water leaks, or pulling the cooker out of position.
You say you have wired the cooker in, which sounds like you have done it recently; so we have to suspect a defect in the wiring such as a stray strand, or an incorrect connection; or a fixing screw coming into contact with a wire; or a fault on the cooker - is it new? Did you experience RCD trips with the previous cooker? Has the cooker been stored in a damp place?
Another point - does the Cooker Control switch on the kitchen wall have a socket built into it; and, if so, do you have anyuthing plugged into it? (if so, please unplug it).