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You are correct, in that it means that if either of you were to pay more than 50% for any Bill/expense/mortgage payment, then credit has to be given to them by the other party.
In practical terms, if you were to pay off a lump sum of the Mortgage, you can't ask your co-owner to make a similar payment, but you will need to keep a record of the payment, so that you get reimbursed 50% as and when your co-owner can pay it or when the property is eventually sold.
I hope this assists and sets out the legal position.
Correct- if you think about it, you are putting down £20K, £10K of which is "your payment" and the other 10K is the amount your co-owner is legally obliged to pay.
You will therefore get 10K back from your co-owner and you will also have benefitted by the other 10K by way of more equity coming back to you.
Does that make sense?