Spur for a double socket

Hi all, sorry another spur question.

My son has a gas hob and an electric built in oven. Ovens died (very old) and gas hob is old.

The oven (and cable for the auto lighting thing on the gas hob) cable goes into a round junction box which has one 1.5mm T&E coming out of it.

Turning off downstairs sockets in the fuse box also turns this off, so must be a spur from somewhere (will need to remove kitchen units to find where it goes.

The replacement oven comes with a 13 amp plug and says it can be plugged into a normal socket.
Thinking of changing the gas hob to electric, can also get a hob fitted with a 13amp plug.

I presume I’m right in thinking 1.5 T&E is too thin to have both of these plugged in. That being the case, if I replace the 1.5 T&E with 2.5 T&E and replace the round junction box with a double socket, is it safe and usable to have both the oven and hob plugged in? Or will I find if the ovens on, two saucepans boiling away and I stick the kettle on, I’ll trip the fuse?

many thanks

 

Many thanks

As the gas hob works and he’s getting a new kitchen probably next year, I’ll put on a a socket instead of the junction box and just replace oven for now.