That is exactly the problem because that curriculum alone is not accepted in the US to be able to write the exams. What I have also been hearing from some nurses is that their school will not let them take the other courses so that they get their proper training in.
Then you have the crazy recruiters that will promise anything to have a nurse sign on the bottom line and then it all falls through. Sure, there are some very good recruiters out there, as well as some that are extremely unscrupulous. Many of the PMs that I do receive are from nurses in the U.K. that are having tons of problems after signing contracts. I get mail from nurses from all over the world and I think what is happening is that the recruiters are telling you over in the U.K. that they will handle everything, but they don't do it in a fashion that I would. They wait for you to do one thing, then they go onto the next. All should be submitted at the same time. There is no reason that you can't. Especially, you sdon't even have to take the English exams, and my students do. Everything actually tells you to do it as soon as possible.
Visa Screen application, as well as the handbook, state that is your goal is to work in the US in the near future, submit this application as soon as possible.
There is no reason to wait until you have completed your exams. This is especially true if you are not going to write CGFNS exam, and only NCLEX.
If you do the work yourself, then you have the choice of going wherever you want in the country, not where your agency has a contract with. Many of the better hospitals do not use this type of recruiter. Money is being paid to the agency, shouldn't it go to you? You can negotiate a much better deal yourself. Remember the money that is going to the agency would have been going to you.