Jonny, the basic issue is this:
A computer has to be babystepped through everything- it is not instrinically 'aware' of what you want to do with your data until you tell it what to do with it first.
So, for auto-completing a form on website, it would have to know where to put the cursor, and insert in appropriate data, among other things. This is also why other suggested a product because they already automate what you would have to write yourself.
I would imagine it'd be actually easier to just save the webpage after you've filled it out yourself, print it out and file it in your cabinet. But if you really want an electronic record, you will need to decide if you want to learn some programming to move cursor around, inserting text automagically, or just buy a software to do this for you.
There may be free software if you look hard enough, though. I've yet to meet a shareware I wished I had.