Both statute law and contract law come into this.
As far as statute law is concerned, your employer can fail to pay you for the hours worked as long as your average pay, over a 12 week period, doesn't fall below the National Minimum Wage. (Similarly, it's lawful for employers not to pay you a single penny for any overtime worked, as long as your average pay doesn't go below the NMW).
However statute law also states that your employer must provide you with a 'written statement of employment particulars' within two months of starting work. That statement will define the contract which exists between you and your employer. If that statement defines an hourly pay rate, and states that you'll always be paid at that rate, then you should be paid for the morning's work. However if that statement makes it clear that you will receive no pay for 'part days' then, as long as your average pay doesn't fall below the NMW, the employer is no obliged to pay you.
Chris