Solicitor is wrong.
It is not so much the outcome that counts, it is the EVIDENCE and INFORMATION in the DWP case that will be relevant and which you can most certainly rely on. It will be for a Tribunal to determine the weight that should be given to the evidence. You’ll need to get copies of all the DWP paperwork, plus copies of the Tribunal’s decision and, if issued, the statement of reasons.
However, there is one potentially major problem with the LA case – the delay may mean Article 6 of the HRA has been breached. You may have been ok with a few months, but 4 years?
Also, you mention an appeal “…from solicitors….”. Is the appeal signed by the clmt? An appeal MUST be signed by the clmt. At a push, it may be ok if the appeal itself was accompanied by a signed authorisation (dated at the time of the appeal), but a “general” authority to act is not sufficient.
Regards