I have a (quite standard) TR-010X T6360A thermostat that looks like this:
And this is the wiring diagram:
Can I install the Heatmiser PRT-TS WiFi Touchscreen Programmable Thermostat? This is the wiring:
Since you're using a line voltage thermostat, there should be no problems doing what you want.
Most folks run into trouble switching to a WiFi thermostat, when the power from the thermostat is supplied through a transformer in the furnace/boiler. Since this is a line voltage thermostat, both ungrounded (hot), and grounded (neutral) conductors should be present at the thermostat.