Annual deaths from radiation from smoke alarms in the UK?

Zero.

If you took out the sensor and swallowed it, it might cause some harm, but with it stuck on the ceiling the radiation density at ground level is less than background levels. The granite worktop in your kitchen is a greater radiation hazard.

The radioactive source emits alpha particles the air between the electrodes is ionized by the alpha particles a current flows between the electrodes - the alarm stays off a fire starts and smoke particles absorb the alpha radiation the circuit is broken so no current flows the alarm sounds

Some smoke alarms contain an Alpha source. Alpha is very short range and can be stopped by a sheet of paper. So unless some fool is taking one apart and eating the source the answer is none

Nobody dies from the microscopic amounts of Americium in smoke detectors. Your body is more radioactive than it is.

As smoke alarms don't give off radiation.

Nil

zero

.