The worst solution is probably phase control because it introduces a LOT of harmonic frequencies on the mains. Gating the number of power line cycles over a fixed period of time, the "burst mode" solution mentioned by
@Alec_t, is the method used by most consumer microwave ovens to control the
average microwave power delivered to the cooking chamber. Typical fixed time periods are on the order of one minute, and cycles should be gated on at the zero crossings of the line voltage. For 50 Hz power, there are 3000 complete cycles per minute, yielding very fine control as anywhere from one to three thousand cycles can be gated per minute. Only
complete cycles should be gated to prevent any average DC current in the mains. The most common means of accomplishing this is with triacs or a pair of inverse-connected SCRs.
It has been awhile since I performed "burst mode" or "duty cycle" control of anything, and back in the day we had to "roll our own" logic for zero-crossing detection and cycle counting. Surely there must be commercial equipment available today that will do the same thing better and cheaper than anything you could design and build for a "one-off" project. You would also need to integrate the duty cycle control of the AC line voltage with temperature control of the immersion heater. Maybe someone else here has current experience (no pun intended) in this area? I don't much like most microwave oven's duty cycle control because the adjustment range is very coarse and it doesn't work at all for short time intervals, i.e., cooking times less than the fixed time over which power can be applied, typically one minute. For very long cooking periods it works just fine, so this would be ideal for immersion heater control.
I don't think
@Bluejets comment is valid. Duty cycle control is no more likely to create "surges in the mains" than a simple on/off thermostatic control, provided the electrical wiring and mains supply is adequate. BTW, why do you
need proportional control of an immersion heater? Are you trying to obtain a certain temperature with more accuracy than a thermostat would provide?