Absolutely, Pippa, you are right. tbh, it is the court welfare officer who does most of the work and presents it to the judge/magistrate and so you don't need a solicitor per se.
I think you should go for it. All you need to do is pop down to the court house, ask at the reception for the forms, you fill them in there and then and then I think you have to post them on to the ex, although that might have changed.
I think you should definately consider requestion parental responsibility (you don't have to be a bio parent to do this, any number of people can have it) and contact. I am presuming you are not thinking of custudy, however, if things looked dogdy at home it might be the next step once contact is awarded.
you'll never know if you don't try. And if the new boyfriend threatens you, who knows what he might say/do to the littlun. And if he does (to you that is) then it only adds more weight to your portfolio of evidences that these people are questionably not fit to care for your little girl.