My understanding is that it's not just about financial connection but establishing a relationship 'as husband and wife'. Lack of financial connection is not enough. My OH and I have no financial connection. We have separate accounts, each pay separate bills, and I'm not on the house deeds, not is he on mine. Does this mean that if he went and slept at his mum during the week, and just come to the house over the week-end I could claim single benefits? Of course not!
It's a case of looking at the whole picture and establishing whether they are a couple as defined by dwp. If there were living together before, have children together despite being supposedly separated, the fact that he transfers money into her account, even if it is repaid (ie. supporting her until OP gets paid), not paying any maintenance and OP not interested in chasing it, spending quite a bit of time at her house, going on holiday together, family events etc....
As said, my neighbour got done in the same circumstances. It did take years though, but they were able to evidence that they were definitely acting as husband and wife. I know this because they came to ask us if we thought they were a couple, and I had to be honest and said that yes, we perceived them as a committed couple.
Babyroobs, you obviously work for them, but not sure at which level. If what you say is true, and it is that simple to claim single benefits, then it is not surprised that fraud is supposedly so low, because what is clearly FRAUD is not called so.