there are special tools available that remove locking wheel nuts, working in the trade i have used them before, but as mentioned above, on some wheel types it can be difficult to do without damaging the wheel, and the tool needs to get sround the locking wheel nut, which may not be possilbee depending on the wheel nut type. once its out, you can put one of the standard wheel nuts in for the time being.
elite in rainham are good at this sort of thing, but maybe too far for you to travel, so find a good local alloy wheel centre, who should look after your wheel whilst extracting the nut.