As mneary said, you need to measure voltage as well as current to find the power.
If you are using a PIC, you do not need to rectify the signals. You can read the current and voltage signals plenty fast enough with the A/D converters to follow the 50 Hz mains.
Use a current transformer like RS 537-4536. Put the output into a suitable load resistor and measure the voltage.
The mains voltage can be safely and accurately measured through a small transformer with no load. You just need two mains transformers, one to power your circuit and one to read the voltage.
For both current and voltage you need to offset the voltage to mid rail (2.5V if you are running on 5V) so that the A/D can read positive and negative.
You just read the voltage, read the current, multiply the results, repeat at least 500 times a second and average the results and you have a true RMS power meter.
If you are prepared to guess that the voltage is 230V (its typically about 245 V in the UK even if the nominal is 230 V) then you can read the phase from the mains transformer that is feeding your circuit, but your calculations become more complicated.
BTW, running power meters from voltage and current transformers is common practice. Where I used to work, there was a 3MW, 11kV motor. The energy used by it was measured buy a meter that looked much like the ones in houses, but it was fed from 110V from a transformer from the 11kV. The current was transformed down as well, mainly to keep the 11kV away from everything than to get the current down, but that probably had 100:1 ratio as well.
The result was that the power measured by the meter was 10,000 times less so the meter was just a small unit. That is the sort of thing that you will be doing.