I was in a similar situation 20-odd years ago where I moved in with my partner.
He apparently (not that he told me, I discovered this for myself) knew all about these laws where if an unmarried couple split, if you can PROVE 'significant contribution' you have more rights over financial matters etc.
I told him right from the start that I intended to 'pay my way' and would contribute to the running of the household, food etc.
Not that this is particularly relevant but at that time I did earn more than he did plus I had child benefit for 2 children and disability benefits, so made up more than 2/3 of the household income.
We calculated all household costs (mortgage, utilities etc and food) and 'he' declared that because the children were mine (from previous relationships), I should pay 2/3 of the bills BUT I was NOT to transfer money through the bank, I was to give him my share in cash (thus eliminating any financial trail and proof that I'd contributed).
Initially I agreed and regularly gave him my share in cash until about a year down the line when someone kindly told me that in order to protect myself I should 'insist' on us having a joint account, not for both our salaries to go directly to but one where we could both deposit our share of the household bills and for them to be paid from there.
I put this to him, he wasn't keen but I said it was safer than me giving him cash each month and I told him that if he refused to do this then I'd be leaving! I didn't actually mean that I'd leave him but it scared him enough to make him agree.
We carried on like this for a year or so, then I did actually leave but didn't take anything at all from him other than a few pieces of furniture that I'd entered into the relationship with and went off and bought my own house.
When I left, I know that I could have forced him to sell the house or extend the mortgage to 'pay me off' because I could 'prove' my contribution to the household, especially that I had paid the lion's share but I just wanted rid, so I walked away and left him to it.
That isn't always possible for others in a similar situation so I would always strongly encourage people to ensure they have 'proof of contribution' if they're not going to get married or enter into a civil partnership.