Silly question now perhaps, but do all boilers support these things?
I've started an email enquiry with Honeywell about their products, but
I'm not sure whether my boiler will allow a programmable thermostat to
be fitted.

Every gas boiler ever made that uses electricity can support a programmable
thermostat. They will have one of three methods:

1. "Voltage free" contacts (just connect the thermostat terminals across the
boiler thermostat terminals)
2. "Call for heat" input (just connect the thermostat terminals across the
call for heat input and the live.
3. Main power input (just connect the thermostat terminals between live and
the boiler power input.

(3) Would be required for really ancient type boilers that just fire up when
there is electrical power. Think old cast iron lumps.

Most modern boilers use method (2), as it allows most flexibility in wiring,
although some (particularly combis) use method (1).

Christian.