You dont have to have CSCS. They are not legally required to work on a construction site. They are just an indication of someones competence and safety awareness.
We recently did a big construction site clean and CSCS wasn't mentioned at all, they wanted to see our P/L Insurance, that we were tax registered and then on the day we turned up we had to watch a health and safety video for about 20 minutes; wear hard-hat, steel toe-caps, flourescent jackets and sign our lives away.
This is from the CSCS wwebsite
The CSCS Card shows that the holder is considered to be competent at his or her job, lists any relevant certificate/qualifications and also shows that the holder has passed a health & safety test.