That's the idea.
The Heat link
Contains two simple switches inside, one for the central heating and one for the hot water.
The programmer, hopefully something similar to this...
.....also contains two simple switches inside for the central heating and hot water, exactly the same. So, the programmer is removed and the wires removed from its terminals go to the terminals of the Heat link that have exactly the same function. No additional wires will be required, only what is already there will be needed. [Assuming your existing system is wired and working correctly]
If you don't want to have the Heat link where the programmer is, it can be located somewhere else, but it then becomes quite a major wiring job, not just a simple exchange of one item for another.
The old existing room thermostat needs to be decommissioned to stop it interfering with the Nest. This is done by tracing the existing thermostat cable back to its origin, disconnecting it and then inserting a wire to bridge the terminals where the two live wires that went to the thermostat have just been disconnected from. [If that's too difficult, the old thermostat can be left where it is and set to its maximum setting]
Finally the Nest thermostat requires 12v to power it. It can get this by being wired to the Heat link, (terminals T1 & T2 are provided specifically for this purpose) or by using a separate plug in power supply for it.