Potential divorce post affair. housing complications

ENGLAND I've just found out yesterday my husband of 4 years has had an affair, and I'm looking through various options. Please be gentle, it's all very upsetting right now.

I'm a stay at home parent to an 18 month old, with no income. Before children I gave up work to move for his job at a mutual agreement. This has left me isolated and away from family. I'm aware this is more of a practical than legal issue. We share one bank account that he regularly puts money into.

A month before marriage he bought the house we live in via mortgage with the intenton of it being "our" family home. I was listed as a dependent on the application and am now listed as spouse. I have helped pay for both the porch extension and the rendering work we have completed on the property. We have mirror wills leaving the house to each other or our child if we both die.

Could the house be considered a marital asset? Do I need to make him agree to put my name on the mortgage before divorce proceedings?

If we were to divorce which route should I go down? I can prove the affair as he has admitted it via text and has probably also given me an STI. I am unfamiliar with no fault divorce and what that would entail. Custody would be an entirely separate thing and not an issue.