In this paper we present a parameter estimation analysis of the polarization and temperature power spectra from the second and third season of observations with the QUaD experiment . QUaD has for the first time detected multiple acoustic peaks in the E -mode polarization spectrum with high significance . Although QUaD-only parameter constraints are not competitive with previous results for the standard 6-parameter \Lambda CDM cosmology , they do allow meaningful polarization-only parameter analyses for the first time . In a standard 6-parameter \Lambda CDM analysis we find the QUaD TT power spectrum to be in good agreement with previous results . However , the QUaD polarization data shows some tension with \Lambda CDM . The origin of this 1 - 2 \sigma tension remains unclear , and may point to new physics , residual systematics or simple random chance . We also combine QUaD with the five-year WMAP data set and the SDSS Luminous Red Galaxies 4 ^ { th } data release power spectrum , and extend our analysis to constrain individual isocurvature mode fractions , constraining cold dark matter density , { \alpha } _ { cdmi } < 0.11 ( 95 \% CL ) , neutrino density , { \alpha } _ { ndi } < 0.26 ( 95 \% CL ) , and neutrino velocity , { \alpha } _ { nvi } < 0.23 ( 95 \% CL ) , modes . Our analysis sets a benchmark for future polarization experiments .