Some years ago, Essex had a reputation for refusing transits (and did so to me a few times). More recently, I've had nothing but friendly, helpful responses from them.
If it's going to take me a couple of minutes more to route round CAS, I don't bother to call. If it's a long detour, I do. That seems to work fine every time.
Flower knows better than I do - but I've found that a confident, clear, straightforward call and request will get what's asked for, and a long rambling vague one will more likely get the polite refusal.
One that did surprise me - asking for "LARS" will almost always get a "say service requested" - so I ask for RIS (or RAS if under IFR) and that seems to work fine.