In my country we have very similar queueing etiquette to the one in United Kingdom.
Cutting in line per se is a no-go.
I have experienced this exact situation several times, from both perspectives. My answer will focus on the etiquette and therefore on the person who had to fill out the form.
As I see it, when I'm filling out the form, it is still my turn. To prevent the employee from having to twiddle their thumbs it's fine if they help someone else before they can continue helping me. But it's still my turn so when I'm ready and the opportunity is there, I expect the employee to continue helping me.
But of course, that is usually not explicitly being said in the moment so it is not a clear agreement.
What I do in this situation - if the first-in-line isn't aware of the situation and doesn't let you go before anyway - is that I walk up next to the queue and wait next to the first-in-line and make eye contact with the employee. This puts the onus on the employee to tell the first-in-line to wait so I can finish my turn by giving the filled form. When he does, thank them both (employee, first-in-line guy) with an appreciative smile and nod [1].
This way, you do not have to ask yourself if you could cut the line, which is rude and mostly turned down.
[1] If the employee does nothing after the eye contact, just be patient and wait, while making eye contact as much as possible. But don't cut the line without the employee telling you to. He will do it eventually!