The old wired Honeywell thermostat needs to be decommissioned properly to prevent it interfering with the operation of the Hive. It can't simply be disconnected as this would leave the heating wiring 'open circuit' and it would not operate.
The thermostat can be decommissioned in three ways as described below. Number 1 is the best method and would be the method used by professionals as it allows the complete removal of the old thermostat and the wires going to it. Usually a single 3 core cable is used, however as you appear to have two black wires at the thermostat, it may be that two, 2 core cables have been used instead and one of the red cores have not been used, but it is impossible to confirm from the photos. If you find that you have something different, and are unsure how to proceed, post back what you find.
From the information you posted, the existing Honeywell thermostat terminals can be identified as follows:
Method 1. Trace the thermostat cable / wires back to their origin. Note where the wires are connected, disconnect them all. Then insert a link to join together the terminals where the 'live supply' and 'switched live' wires (those presently going to the Honeywell 1 & 3) originated from. Or...
Method 2. Remove the existing thermostat and replace it with a junction box, connect the 'live supply' and 'switched live' wires (those presently going to terminals 1 & 3) together and isolate the neutral (terminal 2) separately. Or..
Method 3. Leave the existing room thermostat in place and move the 'switched live' wire from terminal 3 and put it in terminal 1 with the 'live supply' wire.