Prescriptions require visiting a doctor. And a chemist. Hardy isn't about to do either in Broadchurch (he'd be put on medical leave, unable to work the case). So, he periodically drives all the way out to Dr. Baxter's office to, ehm, politely ask (really, beg) for more of the little white pills that are keeping him alive.
Alec Hardy lies, but not all the time. Spoilers for the end of Season 1 (episode 8). If you don't know who the killer is, and don't want to know, don't read.
Ellie thinks about her partner
Why is Hardy so attached to his tie?
In which grumpy Hardy muses grumpily (or, falls into the Thinking Spiral of Doom)