Can you connect a double 13A plugs to a previous un-switched cooker outlet, coming of a 45A

That will be fine as the breaker rating is more than adequate to protect the load that a double socket could potentially draw. However, you would have to keep the existing cable size.

No because the cable used will be of different size I would imagine and will just burn out. Potentially causing a fire !! Hire an electrician

Hi It's a NO you can't do that. You will need an electrician to reduce the 45a to a 13a point by adding a max of 20a fused switch fed from the cooker outlet, then you can add the double socket fed from this fused switch to be used to plug in the cooker IGNISION only ( NOT THE OVEN ) or any kitchen appliance that requires a 13a feed and doesn't need to be hard wired such as a dishwasher or washing machine referring to the manufacturer. instructions.

Yes, but make sure what you are planning to plug into the socket is designed to be plugged in.

Yes but you should replace the protective device with a 20 or 32amp MCB/RCBO

I would recommend that you call a local electrician to install

Any of us professionals could yes. As for you doing it, I don’t actually know.

If the cable is 6mm I would connect a 13a socket to it & change the fuse/mcb rating to a 16a. Alternatively you could fit a 13a switch fuse spur where the cooker switch is then run as many sockets as you like from the load side as you like. As with all things with our regulations a lot of checks need to be done first, bonding is all upto standard, a 30mA rcd is installed & it disconnects within the right parameters

I would seriously consult with a qualified Electrician to make the necessary changes to the circuit before hand.