There is no simple answer to your question.
I suggest that you increase your salary, but keep your honesty. If you are not forced into giving an answer in the application process you could answer the application process question by saying something like 'CURRENT SALARY: To be discussed in person'.
Giving a market rate in negotiations is probably a good idea but you have to decide when it is best to do this. Doing this too early risks turning off the employer pre-interview and might, or might not, be considered 'too clever by half'. From their perspective 'pretty overblown statements of achievement are fine in glossy graduate recruitment literature' but not on CV's, so they might, or might not, be reluctant to hear market rate figures from someone that they have not yet met or requested it from. Play it by ear, and make sure that your source for the 'market rate' is reliable and from a respectable source of independent figures.
If they demand an answer to this question before meeting you it probably tells you something about the organisation. Some application technologies do not process applications without this figure, which suggests that the organisation tends to be good at implementing computer software for process control, but is not so good at listening to people outside of the box.
The majority of employers probably would use this information against you and to drive down an offer. In the application process it would be used as a quick assumption to reject applicants (e.g. current salary too high or even current salary too low). In interviews, if they realise you are underpaid it might be a case of 'well I can pay you a bit more but not quite what you might have been expecting, yet'. That way they drive down the offer and hope to convince you that they're generous.
Ultimately you should focus more on convincing them about how well you can do the job. If you do not think it is all about current salary then prove it to them. The current market is less geared in favour of recruiters than a few years ago. Many good employers see 'current salary' as a criteria, but not the only way of determining where you would fit in an organisation, and as you probably know others do not even request it. Personally I think that it is a bit narrow minded and short-termist to consider it as 'hugely helpful'. That view rejects the future and too many other aspects of organisational management. Good luck with your salary negotiations and do what you think is best after considering all the options.