Hi,
The living allowance payments and travel costs received from the partner organisation are third party expenses/benefits and they are taxable.
EIM20503 - The benefits code: "by reason of the employment": expenses paid and benefits provided by someone other than the employer: third party benefits - HMRC internal manual - GOV.UK
However if the payments qualify for tax relief in full there will be no additional tax to pay.
When travel qualifies for tax relief (
490: Chapter 2) - GOV.UK
You must be able to demonstrate that all the money received qualifies for tax relief by keeping adequate records.
Employees’ responsibilities for travel expenses (
490: Chapter 12) - GOV.UK
When you complete your Self Assessment return Employment section you will need to include the amounts paid in the 'other benefits' box and then claim the tax relief in the 'Other expenses and capital allowances' box.
I would recommend putting a bit of narrative in the 'Any other information' box in your tax return to explain the circumstances of these entries.
Thank you.