A little detail....

P = U x I x COSINE phi

A current transformer seems to be a good option. Because you need a galvanic isolation from mains.
You have to measure the voltage over a piece of wire (=little resistor) and the (rectified)voltage from a voltage transformer. You need the time between 2 zero-crossings fot calculating the cosine phi.

You can use a lookup table, becauce a cosine is quite hard to calculate.

I have seen a midfrequent drive for induction heating and the device uses this way to measure the output power.

Succes with the project!!!

koen