Hi,
As per the guidance held at
PIM1030 if you own a joint rental property but are not married or in a civil partnership with the joint owner then you are not required to obtain a Deed of Trust or any other paperwork.
The rental profits can be split in any way that the two of you agree.
Although it may be prudent to have a written note of the agreed split (which can be altered each year) you will not be required to submit this to HMRC in respect of your income from property.
Thank you.