Thanks or your question
In this instance this work you are undertaking sees you both being wrong, as were it not for this umbrealla company they insist on OR your limited company, you would in fact be their employee and should be paid (with tax and National Insurance deducted) under PAYE. (You would not be CIS as you are not working dicretly for the contractor - but the third party agency)
This is due to the fact that this breaches employment lstatus legislation - for which I add link above and may also breach IR35 legislation
And so many employment agencies are breaking the law themselves and also that of the workers they engage
I would remin refusing to sign the documents and state that unless they pay you, UNDER PAYE you will take the matter both to ACAS (Employment law specialists link here http://www.acas.org.uk/index.aspx?articleid=1461
and approach HMRC to review their working practices.
If you need to speak to HMRC ring as soon after 8am or as close to 8pm with a better chance of getting through almost straight away
Let me know if you have any follow up questions on the information I have provided.