For example, if Mr A owns a property jointly with his girlfriend Miss B and they agree to share income 20:80 then if Mr A incurs £100 paying (in full) for a property repair then clearly £20 is deductible but is the other £80 also deductible? Has Mr A incurred the other £80 wholly and exclusively for the purposes of his property rental business or (at least in part) for some other reason such as personal reasons connected to his relationship with Miss B? On an arm's length basis you would not expect Mr A to pay any more than £20, but perhaps that illustrates why he may have a problem deducting the other £80.
An interesting point; my view is as follows.
Assuming that A and B agree to split income 20/80 and expenses 20/80 (which wouldn't be unreasonable) then A in your example can deduct the 20 (ie his share of the 100 expense) but not the 80. The 80 has been discharged by A on behalf of B as under the agreement expenses are to be borne 20/80.
B can deduct the 80 but is in debt to A for the 80.
The 80 A incurred was not "wholly and exclusively" incurred by him in respect of
hisproperty business albeit for
the property business.
If, for whatever reason A and B agreed income split 20/80 but no mention is made of any expense split, I would still argue that they are not each free to discharge expenses in any old manner and that for tax purposes prima facie in the absence of any other evidence to the contrary expenses should follow the income split; hence, same result as above.