I'm a huge fan of EDC and consider Martin to be Briers' best characters. Definitely more complex, nuanced and observed than Tom Good.
The whole idea of Paul pursuing Anne isn't a sincere one. He's a bit of a suburban playboy, granted, but his affectionate flirtations with Anne are mere friendly teasing, given how he knows deep down that Anne would NEVER cheat on Martin. He does however recognise that she gets awfully frustrated with Martin's nature at times, so likes to remind her that she's still a fun, playful and attractive woman, just so she's reassured that her marriage hasn't dulled her character to that of a dowdy doormat...if that makes sense?
In the first series, Paul's at his most louche around Anne, but as the friendship between all the characters builds over time, he drops any sincerity to his flirting