I've just received peer reviews for an applied paper that reported a table of multiple linear regression coefficients. While I reported 95% confidence intervals for these coefficients, a reviewer has requested I report exact p-values as well. The difficulty is that the confidence intervals were estimated via an ordinary non-parametric bootstrap, given the peculiarities of the data set.
Is there a way I can estimate 'pseudo p-values' from these confidence intervals? If so, under what assumptions/conditions are these p-values reasonable?