That's a standard backplate wired up for a system with a 3-port motorised valve (Y-Plan). The functions of the wires connected to it can be identified from the diagram below....
....the wires are moved from there to the Heat link terminals that have exactly the same function as per the diagram below ['CH On' is the equivalent of 'Heating call for heat' and 'HW On' is the equivalent of 'Hot Water call for heat' 'HW Off' is the equivalent of 'Hot Water Satisfied']
You will also need to link the Heat link 'L' to the two 'common' terminals 2 & 5. (The existing programmer has these links already made internally)
If you want to power the Nest thermostat from the Heat link, then an earth wire is required and connections to T1 & T2. If you use a separate power supply for the thermostat, these aren't necessary.
If you have an existing room thermostat, that either needs to be left in place and set to its maximum setting, or if you want to remove it you can, but a wiring modification will need to be made to 'bridge' the open circuit left by its removal.