Sorry to disagree! No he cannot claim, but if the family income is low enough to mean that there is a potential claim, then the two of you can jointly make a Tax Credits claim.
In respect of a couple living together, a Tax Credits claim must be made jointly. For just one of a couple to make a Tax Credits claim could amount to benefit fraud.
The joint claim for Tax Credits is not a problem in your circumstances. It would not infringe the "No recourse to Public Funds" restriction on your visa.
The income limit? Assuming there is just one child in your household, and do appreciate that the new UK tax year started today, the cut-off point for Tax Credits is now about £26000. But it is quite a bit more than that if there are more than one child in your household.
You mention Tax Credits, but what about Child Benefit? Is that already being claimed in respect of your daughter?