The simplest way to work this out is not to think of splitting the equity, which will vary over time, but separately splitting the ownership of the property and the responsibility for the mortgage, both of which can be given stable values as described in this excellent answer to another question.
With the values you've given the house is now worth £400K, of which £180K is your partner's current equity, and £20K is your current equity. Of the remaining £200K, you expect to pay it off equally, i.e. you are both going to contribute £100K (the actual amount you will pay will be more, but in present values based on the loan you are taking on, £100K is right).
So overall, your partner should own £280K/£400K = 70% of the overall house, and you should own £120K/£400K = 30% of the overall house. And along with that, you both have 50% liability for the mortgage.
If you later split up or sell the house while the mortgage is still running, you then need to calculate your actual equity at that point based on those percentages. For example suppose the house has fallen in value to £350K, and the mortgage is now £100K. The ownership of the house is £105K to you, £245K to him; and the responsibility for the mortgage is £50K each. So your equity at that point would be £55K and his would be £195K, out of the £250K total.
The key thing is that the equity proportions are dynamic and would depend on the house value and outstanding mortgage at any given time. Right now they would start out at 90:10, and once the mortgage is paid off, they would be stable at 70:30, at least as far as your current agreement is concerned. But in between they will fluctuate as you pay off the mortgage and depending on how the house changes value.
In the longer term, particularly if your finances become more mingled or you get married, but even just if you cohabit long-term and this bill passes, you might find that the law overrides that agreement. There's more discussion of those issues in this question.
