I've never seen tanking membrane applied quite that roughly- it sounds like a bodge job. Usually in solid walls you inject from both sides- the modern stuff seems to go into the mortar courses rather than the brick. I suspect they've chucked SBR slurry at the wall then followed it with that membrane- if there is water leaching into the wall from high external ground it'll get above that membrane eventually. Gap between floor and wall- can't see it. Lots of older houses had ground floors concreted (unnecessarily) due to timber floors rotting cos of blocked airbricks or floor voids full of rubbish. Many concrete fills were poor quality- not bedded properly and no DPC (polythene layer) under the concrete so guess what- any water in the the ground will make the concrete damp. Good for its strength, bad for your furniture/carpets.
Did this company diagnose the problem (ie did they survey and give you a list of what needed doing and a quote to do it all)? If yes then they haven't finished the job, ask them nicely to finish it, then give them 14 days notice before action, then (if it's an insurance backed guarantee) claim on it, if it is only the company backing the guarantee then small claims or statutory demand