MrsDV, I found that with Battersea too, long ago before I got involved in rescue myself. I hope they've changed now.
I've met some truly lovely rehomers through the rescue I help out at hands-on. We're lucky as most of these folk are fairly local and being a small rescue they keep in touch with us all, joining the rescue's forum and popping in for tea and cake with our old canine friends, some helping the rescue out in the kennels or by bringing us blankets and the like and, as happened a week ago, many meeting up with us all again at dog show fundraisers.
But, oh god I've come across some asses! Included in these are:
The guy who rang us up to ask if we had an unspayed Staffie as he wanted one to breed with his dog. :( 
The man who wanted an "outside yard dog as a guard, the more aggressive the better".
Several people who want a dog having at their own admission got rid of or had PTS the last one because he was too much hard work/a puppy who weed on the floor, chewed or mouthed/they had young kids... and yes, each of that latter lot still had kids and those DC were still young.
Those wanting a dog despite working full time and having neither provision nor intention of catering for the dog in their absence.
Various people who wanted a dog although their spouses definitely didn't.
A family who wanted an unneutered/unspayed dog or bitch because they "don't agree with" neutering.
Plus those who wanted to adopt without landlord's permission, with the intention of emigrating/moving on with the armed forces etc in the near future, those without gardens or fences in gardens they did have and no ability to erect them owing to land size or planning permissions, those who wanted a specific dog they'd seen on the forum regardless that he was totally unsuited to them (yeah, rescue really wants to home a prey-driven sighthound to a home with cats)... the list goes on.
And as for some of the reasons why people want rid of their poor dogs and the emotional blackmail they try, don't get me started!
So yes, rescue can be a bitch but by god we have to bite our tongues sometimes. And the vast majority of us in the independent rescues and all of those who, like me, act as middlemen in finding and matching rescue places for unwanted dogs as well as those who transport dogs to the safety of rescue are unpaid volunteers who do this in spare time, often to the detriment of our long-suffering families.
The key point is this - if you are a reputable rescuer of any sort you do not work for the owner who wants rid, nor for the prospective owner... you work for the dog and you will always put his best interests first.
And breathe. :)