Result = melted cable in Cumbria?
the cooker mcb will be around 40A which is way too high to protect a 2.5mm² T&E cable, fit a 16A mcb
You have to remember that current is drawn by the device being used not pushed by the circuit (like voltage is). So while the cooker circuit can supply 40A the welder will never draw that mug and the 2.5mm square cable will handle the current being drawn by the welder just fine.
However it's not ideal because if you wire something else into the cable that draws more current it will supply it until something catches fire! As long as you only use the welder on it you will be ok.