GBP 4,100 can't be right. Are you sure this is for the p1 and not the regular series Mclaren?If the factory made a "factory mistake" and upon delivery neglected to supply the mains cable, surely they would have rectified their mistake by sending the cable afterwards, in which case it should now be available with the charger, should it not?
Beyond that, your cost estimate of "around GBP20,000" is laughably high. Below is a grab from the official options price list.
Perhaps you should try another car forum, as I doubt that your pitch will get you very far on this one.