@ Gloria
The point is, op would still have to contribute towards bills. So she does not have £500 a month all of a sudden.
She intends to buy 1% at roughly 70k. I currently live in SE and it's a myth that property prices will keep going up. Also, I lived and worked outside the SE and I know 70k could buy you a ready to move in rental flat with high equity and decent net yield.
OP has a very good arrangement and she should avail the situation and save for her own nest egg. Even, if she "plays her game right" she could even get partner to free up some cash in form of "soft loan" towards her own nest egg & put a hefty deposit down or buy outright all in her own name.
Let's look at it realistically:
she cant afford to buy equal share on current house which makes it unattractive proposition for someone who owns outright (and doesn't need the money as OP stated).
OP admits the house would rent for 2k ish a month
She also admits they both incur bills and spends to which she contributes the £500 and partner adds to that, which I presume is more - unless OP says otherwise.
I'm afraid OP is about to ruin a very good arrangement. As for getting married,1% equity will not impact how she'd be treated by the courts if they eventually gets married then divorced. She'd be favoured by the courts anyway given time together, age of kids and other factors.
Neither would 1% equity affect how her partner would treat her in future if they split whilst not legally married, the 1% is insignificant to someone who owns 99% outright! So he could still be a dick if he wanted to! As Even without an income he'd still be able to raise finance and buy out the 1%.
To think OP doesn't have rights because she's not legally married is naive. They've lived together for years and have kids ffs.
OP, please seek professional advice. This is a place you come to if you need reasons to get divorced! It's disrespectful of some of you to accuse OPs partner of living A subsidised life at her expense! I guess that's come from stay at home mums who don't contribute at all. Op is contributing at a subsidised level as she admits, and it's better for her to buy rather than push on this silly 1% equity on current property.