Don’t know anything specifically about code of ethics for English solicitors, but it wouldn’t fly in Canada.
Nothing wrong with the police officer doing the initial interview, unless he knew that the detainee was already a client of his partner, but it’s not common for most people already to have a lawyer when they’re first picked up, so that’s my assumption. If so, no reason for the officer not to do the interview.
Different for the solicitor. As soon as he realised his partner did the interview, he’s off the case. The lawyer owes a duty of undivided loyalty to the client. That duty is compromised if the lawyer is closely connected to a key witness.
Most cop/lawyer shows ignore conflicts of interest because they want the emotional and ethical issues raised by the conflict to drive the plot. That’s exactly why codes of conduct forbid acting when in a conflict - those emotional and ethical issues can undercut the lawyer’s foremost duty to the client.
ETA: just realised I’d misread the OP - thought the officer did the interview, not the arrest. Even so, same principle applies. An issue could come up about what the officer saw, why he arrested, and so on. There’s always the potential the accused has a different story about the arrest, and therefore the solicitor shouldn’t act.