Husband wants 50% of house deposit during divorce but didn't contribute to it

OP, he is not automatically entitled to half.
He is probably entitled to something. He has contributed to the mortgage in each property which means that he has, indirectly, contributed to the equity which was used as a deposit.

When a court looks at this type of issue, the Judge has to come up with a settlement with is fair to both of you, taking into account all relevant circumstances. In this case, those circumstances would include the fact that this is a relatively short, childless marriage, that you made higher capital contributions, that he has higher income and earning capacity (and therefore, presumably, higher borrowing capacity)

A court would also look at your respective needs - you both need somewhere to live.

A court would look at all assets, so his pension (and yours, if you have one) would be relevant too.

It would be sensible for you to look at what you could afford - how much of a lump sum could you raise without having to sell your house? You have over £80K equity - look at whether you can increase the mortgage (possibly by increasing the mortgage term) so you know what your 'bottom line' is, in terms of any negotiation.