In my experience (multiple cars), it's just a button that you flick and the ECU (presumably) sets it.

....can the driver control the force with which the brake is applied, or does the ECU decide?

Nope - not on mine (a 2005 Audi A8). It's either on or off. You don't even have to switch it off when moving off as it disengages automatically.

For fear of wearing it out I hardly ever used it, perhaps once a month or so to keep it moving. However, this was clearly a bad idea because when needing new rear pads last year at 76,000 miles, the caliper was found to be so seized the indy couldn't insert a new pad......£500 to sort! (including new pads) Still, can't complain; biggest bill so far in ten yrs ownership.

My 2010 Insignia it was possible to add a little extra clamp by operating the button a second time

There is an accelerometer in the ECU that will detect movement and clamp harder if required

How do electric handbrakes comply with the C&U regs?

The parking brake shall be so designed and constructed that—

......in the case of a motor vehicle, its means of operation (whether multi-pull or not) is independent of the means of operation of any braking system required by regulation 18 to have a total braking efficiency of not less than 50%; and

........ its braking force, when the vehicle is not being driven or is left unattended ...... can at all times be maintained in operation by direct mechanical action without the intervention of any hydraulic, electric or pneumatic device and, when so maintained, can hold the vehicle stationary on a gradient of at least 16% without the assistance of stored energy.