As everyone says, srndard size ovens are under 3Kw and fine plugging in, or wiring in, to the ring main. Your existing one is wired in to a switch, does that switch have a little slot or drawer type thing for a fuse, in which case its a simple fused spur, or is it a specific cooker one which probably says ‘cooker’ on it and is rated higher?
Do you know where your consumer unit/fuse box for the house is? are the fuses labelled? if not, do you know which fuse it lights, ring main etc? if not then work it out by removing a fuse at a time and seeing what no longer works around the house. Its common practice to split the sockets in a house in to 2 or even 3 (kitchen, upstairs, downstairs, or kitchen, front half, back half), lights are one or better 2 (up and down stairs), oven on its own circuit is good but not essential for 3kw and under ovens, HW immersion heater will be on its own circuit, and then outbuildings should be on there own circuit.
its sounds to me that your not have an issue with the wiring, but you do need to work out which circuit to isolate before removing the old oven and installing the new….or you may find your hair stands on end and starts smoking