Ok, so here's the update.
I was contacted the day after my demo area clean (see top of thread) to be told that I had cleaned the worst of the three areas set aside for demo cleaning

and that mine had come up the best

Today I went to see the first area out of the 9000 square metres they want cleaning. Price agreed £2.10 per sq metre plus vat.
The FM was at pains to acknowledge that he knew it wouldn't be perfect even after cleaning.
To answer some of the other points raised earlier in the thread we also discussed the length of time to undertake the job and how many bodies may be involved. His reply"the price is fine-if you bring more bodies in and complete the job in a quicker time then that is of no interest to me."
We then had a fruitful discussion about how/when to schedule further work and what type of cleaning methods may be used then. Finally he had no problems in paying normal rates if for example somebody has a major spillage the day after this big clean.
I just wish all clients were so pragmatic, although I guess that having gone through the test area trial it did put me in a far stronger position for negotiating as they would otherwise have to start trialling other cc again.
Rog