I don't know what electrical connection you are showing in your photograph, But the wiring terminals to the boiler for an Ideal Logic + Combi should look like this.
In your case the existing thermostat cable should also be connected into these terminals. This is no longer required, disconnected completely and removed.
The N & L 230V mains supply for the Hive is connected into the N & L above, along with the existing wires providing the 230V supply from the 3A fused spur.
The link shown on the right, in the terminals marked 'Room Stat Timer' (or any wires in those terminals from an existing thermostat) is / are removed. Then the end terminal shown on the far right connects to the Hive terminal (3) 'Heating On' and the terminal next to it, connects to Hive (1) 'Common'
If for your boiler, you have to open up a room sealed enclosure to access the boiler wiring terminals this should be carried out by a Gas Safe engineer who will make sure that it is sealed up again properly afterwards.
As an alternative, it may be possible to connect Hive to the wires that go to your existing thermostat, provided that it has a 230V supply. (Some thermostats do, some don't)