The 3rd party is generally the other insurer(person that hit you), if his insurers have arranged for an engineer to inspect your vehicle it doesnt necessarily mean that they have accepted liability, they could just be speeding the claim along and seek expenses from your Insurers if the claim is paid
Ask your solicitor for the 3rd party insurers details and call them directly for an update.
Every insurance company works differently and there is no set rule on claims procedures.