The existing cables are HDMI cables and coax/sky. Does this sound right
AFAIK, if unsheathed mains wires and low voltage (eg HDMI and coax/sky) wires are enclosed in the same conduit or trunking, then the regulations require the low voltage wires to be sufficiently insulated to withstand mains voltage.
If you are just considering the space under floorboards, the mains cable they are installing will need to be sheathed, so there should be no electrical safety reason why it should not share the space with HDMI and coax/Sky cables.
However, they may be worried about any interference induced into the HDMI and coax/Sky cables from the currents and voltages in your proposed charging point supply cable. How far apart could you keep the cables?