your walking (or lack thereof) sounds pretty similar to mine.
200m is about the length of 20 double decker buses. That’s a blooming long way. There’s no way that you set off in your home and walk 200m in one go.(unless you live in a very different home to mine)
Your consultant really shouldn’t have bandied about distances based on nothing more than chatting to you because the higher mobility figure is 50m (about 5 double decker buses) however he did qualify it by saying hanging on to furniture etc. You will have to give a very full answer on the PIP form (don’t be afraid of using extra sheets) to ensure that the DWP don’t latch onto that 200m and look no further. When I was filling in my ESA application I measured the distance to my shed (about 12M) and then set about trying it out. On the form I put how far I could walk with no aids, how far with a stick and how far with a rolator.
Walking, or furniture surfing in your own home is one thing but the walking question should be considered as getting from a to b on a flat footpath - outside. You must mention how fatigue and safety affects you and also consider repeatability. If you can walk 50M once could you turn round and do it again, without a rest? The length you can walk is how far you can go before you have to stop for a rest or when your legs no longer move correctly ( after so far my feet get jumbled up and that’s the time to stop or I’ll be kissing the pavement)
If you want your consultant to provide supporting evidence for your PIP application I would try to clarify the 200m issue with him. I suspect that he has the old DLA distance in his head and was not aware of the new 50M distance. I don’t for a moment think that he was trying to burn you, just didn’t know. It would be better if he left M out of it altogether because it was a made up distance after all.