(2-part post):
Your store manager is probably simply following the company rules. It's unlikely that he's given any flexibility in the matter. You should therefore contact somebody 'higher up', who has the power to change the rules (or to allow flexibility with the existing rules).
Here's a suggested letter:
"Dear Mr Bloggs,
I write to advise you of an apparent conflict between Tesco's uniform policies and those it has on hygiene.
Tesco, quite rightly, expects its employees to maintain the highest standards of dress and personal hygiene.
However, even though I normally work 5 days each week, Tesco has restricted my uniform allowance to a single shirt (plus two fleeces and one pair of trousers). This is because my regular contracted hours are only from 7am to 4pm on Fridays, despite the fact that I'm normally called upon to work additional hours from Monday to Thursday.
As a result of this policy, I'm effectively forced to wear the same shirt for five consecutive days, which clearly conflicts with Tesco's policies on dress and personal hygiene. (The only alternative would be for me to wash and dry the shirt every evening. This is obviously impractical, in regards to both time and expense, as well as an inefficient use of our planet's limited energy resources).
I therefore ask that the company's policy on uniform provision should be revised and, in particular, that I be provided with additional uniform shirts as soon as possible.
Yours faithfully . . . "