acknowledge the support of the Royal Society. SF, MC, KPL and WGH acknowledge the support of STFC. We are grateful to Xu Kong for help in matching photometric filters and also to Kaz Sekiguchi and Hisanori Furusawa for the Subaru data used in this study. We also extend out gratitude to the staff at UKIRT for their tireless efforts to ensure that the UKIDSS surveys are a success. We would also like to thanks the anonymous referee for their thorough reading and useful comments.

Appendix {#appendix .unnumbered}
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In this Appendix we describe the Fourier method used to deconvolve photometric redshift errors from the n(z) distribution, which can then be used to invert the Limber equation. The errors in the photometric redshift distribution are assumed to be Gaussian and it is also assumed that the measured distribution is simply the convolution of these errors with the true redshift distribution. Under these assumptions it should be possible to deconvolve the errors from the measured distribution, using the fact that a convolution is simply a multiplication in the Fourier domain. Dividing the Fourier transform of the measured distribution by that of the Gaussian errors, should then give us an estimate of the 