You don't need a lawyer to follow the procedure indicated in my post #15, so long as you are sure that LL is liable for the repairs.
Have you checked whether you are likely to be eligible for Legal Aid?
I also think that you need to be persistent with the EHO because they have the authority to enforce the LL's liability for disrepair and they do it for free, - that's their job, to enforce repairing obligations - so that has to be the cheapest and easiest option. Even if EHO has been crap so far, be persistent. Dogged persistence may sometimes be the only language that some council employees understand.