The choice of wire colours that have been used is unusual. Normally the Red wire is used for the 'Live Supply' and the Yellow as the 'Switched Live'. Yours are connected the opposite way around. So, either:
a) The thermostat is wired correctly but the original installer chose to use non standard colours, or
b) The red and yellow wires are in the wrong terminals. At the moment with the Honeywell, you will get away with it if the wires are transposed. (although it won't work as accurately as it should) Not so with the new one.
Ideally the wires should be tested by someone competent with a multimeter to determine which wire is actually the 'live' and which is the 'switched live'. However, if you can't do this, you can proceed on the assumption that they are correctly connected now and move them over to the terminals that have the same function on the new stat. If it doesn't work, simply swap the red and yellow wires over.
From the Honeywell diagram below.....
.....the terminals are identified as:
Live wire (Yellow?) = Honeywell terminal 1
Neutral wire (Blue) = Honeywell terminal 2
Switched Live wire (Red?)= Honeywell terminal 3
And for the new thermostat.....
.....the terminals are identified as:
Live wire (Yellow?) = New stat 4
Neutral wire (Blue) = New stat 3
Switched Live wire (Red?) = New stat 1
NOTE: When the new thermostat is installed, any existing heating time control / programmer elsewhere should be set to be permanently 'on' 24/7 otherwise it will stop the new thermostat from working. The new thermostat should have the facility to provide both time and temperature control (so the old programmer will be redundant anyway) If it doesn't, have time control, you have a problem and some rewiring will be required.
As well as the unusual wiring colours, you have also chosen a rather unusual replacement thermostat. The diagram on the back of the new stat shows it connected to an electric resistive form of heating, such as underfloor heating, hence the extra neutral terminal N1 (2). It also has two terminals (5) & (6) for an NTC (thermistor) again used with underfloor heating. As this thermistor won't be present you may find that this feature will need to be deselected from the thermostat's menu settings.
However, from previous reports of similar devices on this forum, this type of thermostat does seem to work OK with boilers. I have assumed here that you have a boiler, although you haven't said what the thermostat it is actually connected to. You may be using it with electric underfloor heating.