As I've already said in the electrical forum, this could be a far more serious fault than a simple lack of bonding.
When the pipework entering the house was metal, it would have had the ability to introduce an external electrical potential into the house, hence being an extraneous conductive part and the need for bonding. Although we still bond plastic incoming water mains, we only do so at the point where it becomes copper, and more and more often this doesn't happen until inside the house. If anything, your new pipework should be less likely to introduce an external potential.
I suspect that, in actual fact, the water main coming into your house had previously been providing your main earth connection. As it is now non-conductive, any earthed metal parts in your house connected to the electrical installation are free to float at whatever potential they wish with respect to true earth. Worst case scenario is that a Live-Earth fault could develop - this would cause all earthed metal parts to become live, but because of the lack of an earth connection, the protective devices in the installation would be unlikely to operate.
Right now, you're probably just receiving a tingle from currents that are capacitively coupled into the earth, as well as the current dumped there through filters in switch mode power supplies and the like as found in computers. If a more serious fault were to occur, all metal parts could become live at 230v and provide far more than a tingle.
The fact that you're getting shocks from the sink AND the dishwasher/washing machine lends even more credibility to this theory, as they will only be linked to the water main by means of a plastic pipe. The water in the pipe over the length of the flexible hose would be unlikely to be conductive enough to introduce a potential into the metal casing of these machines. Even if it did, the presence of a true earth connection would prevent the voltage on the casing rising to the point where it's able to give you a shock/tingle.
I expect if you were to touch other earthed metal parts such as the screws on your sockets, you'd receive this same tingle.
I think you need the installation checked over by a spark as a matter of urgency. As a bare minimum, he should perform an earth loop impedance test to determine the Ze of the installation.