Samantha, I would have another look at the wording where you claim they are obliged to move you. I suspect (but may be wrong) that the wording is along the lines that they will "help" "facilitate" or words to that effect for those that are overcrowded. the phrasing is important, it doesn't mean you will have a position to necessarily force them to move you ahead of others, just that if you ask, they will assist, it's not a guarantee.
What it probably will mean is that you will obtain a degree of priority, but will then be up against others in the same situation as you, and if your landlord has a high number of bedsits there are likely to be others in identical situation to your own, in which case any extenuating circumstances you have that migh make you more of a priority than others could be a factor.
Time served on the list is usually the main one where you have people in the same circumstances, but any other factors may help oyu, even the point about your disrupted family life due to your partners working pattern might be considered, particularly if others in the list haven't jobs (this shouldn't be to their detriment, but could add weight to yours)
I'd receommend obtaining their transfer/CBL allocation policy and go through it carefully and see what weighting or priority your case should indicate and ensure you provide them with the evidence to back that up.