How do I calculate the equity I have in my home when overpaying on mortgage?

So is there another way of doing this that would also let me calculate the future equity gained based on overpayments?

The equity immediately gained based on an overpayment is exactly the amount of that overpayment.

In general, your regular payment schedule will pay off all the interest for the month in question, plus a varying amount of the principal.

So any overpayments you make will always go in full to reducing the principal and hence increasing your equity in full. There might be some very small effects based on the way your bank applies them, but you can basically ignore those in practice.

You mention "future equity" so perhaps you also want to know how that overpayment benefits you in later months too. Since you've reduced the principal by more than expected, the interest charged will also reduce, which means more of your future regular payments will go to the principal too.

The easiest way to think about it is actually to pretend you have a separate bank account into which you put the overpayments, and that the bank account pays the same interest rate as your mortgage. If you calculate the interest you would have earned on that bank account, including compounding, that's how much extra equity your overpayments have given you.

Just build a pay-off spreadsheet. There are plenty of examples on-line. For example https://www.mortgagecalculator.org/download/excel.php

You can put any optimal payment in for any month and it will show you for each month the amount of interest paid, principal paid, outstanding balance and cumulative interest. Your equity is simply the original loan amount minus the outstanding balance.

Equity is defined simply as the value of your house minus the amount you owe on it. There's not a direct way to calculate this, because you don't know what the value of your house is, without first selling it! But of course you can estimate it, whether by using the purchase price of your house, or other means.

Given that calculation of value, you can then determine your equity by simply subtracting the payoff amount for your loan. This payoff amount is generally easily obtained from your lender; I'm not familiar with the UK, but in the US the lender must provide it to you when you ask, and most provide it on their website on demand. The payoff amount is (principal owed) + (interest unpaid).

Further, you can calculate the daily interest trivially once you have a known principal amount, since that is simply your (daily) interest rate times the principal remaining. From that, you can determine how much of each payment is going to principal, and work it out from there.