If you were to marry, I would suggest that it would be best to alter things to be joint tenants. That way if one of you dies the other automatically inherits the deceased's share without any inheritance tax liability.
https://www.gov.uk/tax-property-money-shares-you-inherit/joint-property-shares-bank-accountss*
There is no inheritance tax (IHT) due on anything left to spouse, a major benefit of being married. This does not depend on how you help the property, as joint or tenants in common.
If you are married and are joint tenants, you will inherit his share of the house and there is no IHT to pay.
If you are married and are tenants in common, and he leaves his share of the house to you, there is no IHT to pay.
If you are not married and are joint tenants, you will inherit his share of the house and there may be IHT to pay, if his share is worth more that the IHT allowance, or that allowance is used up with other legacies
If you are not married and are tenants in common, and he has willed his share to you, there may be IHT to pay, if (as above)
If you are not married and are tenants in common, and he has willed his share to someone else, say DD, they may be IHT to pay, if (as above)
You can get around all these scenarios, for example he could leave his share in trust to DD, with you as trustee or to DD absolutely once she is an adult, and then take out life insurance to cover the IHT.
You both really need a solicitor to go through the implications, say adult DD gets married, then divorced, would you be protected? Etc etc etc.
p.s. can you tell that we got married not for any romantic reason, but to ensure we would each be able to stay in the house, when the first one of us died.