If you aren't permitted counsel of your choice (and he wasn't) but only counsel selected by the police (which he was offered), then you are effectively denied counsel.
> You may as well claim duty solicitors are in the palm of the Police.
While there is still a potential agency problem, duty solicitors (or, in American parlance, public defenders) aren't an alternative to counsel of choice, they exist to provide the choice to have some counsel to people who otherwise would have none, without denying them the choice of securing any of their own to the extent they can.
Providing the option of a duty solicitor is not, then, at all the same as denying someone access to willing counsel of their choice.
If you aren't permitted counsel of your choice (and he wasn't) but only counsel selected by the police (which he was offered), then you are effectively denied counsel.