I wouldn't leave things blank. Assume that if they put a box asking for desired salary that they want you to fill it in.
Presumably it is clear from the rest of your form that you are not currently employed anyway? I would put your last salary in but make it clear that it is not your current salary, so that your form doesn't look inconsistent.
flowery can I ask you why employers ask that question? If you previously earned considerably more than the salary being offered for the job you are applying for would you really be likely to be considered?
I haven't been in paid employment since the mid 1990s when I earned a very good salary plus company car & various benefits; there is no way I would earn that sort of salary now, particularly where I live, and I would be very happy with much less, however I would be reluctant to state what I previously earned. Although as it is so long ago now could I put something like 'not relevant'.
Ragwort I guess that's why ask both questions. If your previous salary was much higher but in the desired salary you put the actual salary on offer, that might be less of a problem.
Asking either question isn't best practice really. Either someone's skills or experience are sufficient for the salary on offer or they are not. What they earned previously isn't usually relevant. It might be if they are utterly fantastic and bring lots of extra to the role, and would not move for less than x, but those circumstances are pretty individual and unusual and not something you'd need to cover in an application form.
Some employers use it to try and get away with paying less, so if they have a job advertised but have not given any indication of salary in the ad, they might use previous salary/desired salary to be able to pay someone less.
Because women have a tendency to be conservative when estimating their worth/desired salary, this is one of the reasons for the pay differential.