Yea that is right, plan is to keep heating on 24/7 from clock and just lowere the temperature through new thermostat to keep the heating on and off.
Then it appears that a smart 'wired' stat may be what you are looking for.
There are battery powered ones available, such as the Tado/TadoX 'wired', where you would only need to make a connection to the brown and black wires (terminals 1 and 3), on your existing stat.
There are multiple mains powered stats from the likes of Heatmiser, Moes, Meross, Bosch etc. but many of these would need a back box, to enable them to sit flush to the wall.
In some cases, you may also need to buy a hub, to enable control via the internet - check before you buy.
But as mentioned earlier, many people we advise on the forum, prefer the straightforward swap of the BG/Drayton programmer for a Hive, or Wiser etc.
In additional to having app control and timing of the HW, the wireless thermostat could still simply be mounted on the wall, in exactly the same position as the old one was.