That's an industry standard backplate, so you don't necessarily have to have another Danfoss programmer, unless you want to. In fact it might be easier if you do choose something else. I haven't fitted a FP720, but the advice is that if you are changing from its predecessor the FP715SI you will need to rewire it using the new back plate provided as the FP720 will not fit onto an existing FP715SI back plate. However it shouldn't be difficult as the wires will go to the terminals of the new programmer that have exactly the same functions as the existing one.
The terminals used will depend on the design of plumbing system that it is controlling. Yours is commensurate with very many in the UK. Some do have a connection to terminal 1 others, like yours don't need it. None, (with a few very rare exceptions, normally old installations) have a connection to terminal 2.
I'll take it that you know for certain that the programmer is at fault, and not another part of the controls such as a motorised valve or thermostat for example.