Tricky one!
I'll operate on the assumption that anything applied / hung will be treated to the best flame retardance standards possible for fabrics. I infer that you supply and install the drapery, so you have control over where it goes and how much of it there is.
The fire properties of wall and ceiling linings will have a massive contribution to make to the speed and extent of fire development in a room, and the thing to remember about the flame retardant treatments for fabrics is that they're generally only intended to make the material hard to ignite with a small ignition source; if subject to a high heat flux, they'll burn quite readily. By lining a room in the way illustrated in the pictures at the link you provided, you will make the fire risk in most rooms worse, perhaps significantly.
The importance of this will depend entirely on the room - ground floor with excellent, capacious and level means of escape may be no problem; poorer means of escape will make things worse; above-ground venues will be likely to be worse, as may basement venues. Delayed evacuation (e.g. for disabled persons where their means of egress is not step-free) requires particularly careful review. So, this might be OK for some rooms / premises, but frankly may not be for others.
So... whose duty is it to make up their minds whether things are acceptably safe? Ans: all those who have 'control' over the fire precautions in the premises. You are one of those persons, as you're the one supplying the drapery and installing it; it's therefore my interpretation (remembering that I'm not a lawyer, so this is open to interpretation and if you're at all unsure you should take legal advice) that, under English fire safety law, you (if a sole trader) or your Company would be one of the 'responsible persons' (RP) mentioned in the Regulatory Reform (Fire Safety) Order 2005. If this were the case, you should have a written assessment of fire risk for every job you do, and you should co-operate and co-ordinate with the other RPs in their control of the other fire precautions - especially those who are primarily organising the event, who should have similar documents of their own. You don't have to solve all the other RPs problems upon their behalf, but you do have to make sure that what you're doing will enable the premises to be maintained acceptably fire safe.
If I were you, I would have a standard list of 'Do's' and 'Don'ts' that you share with everyone (e.g. no naked flames, no pyrotechnics of any description, all portable electrical equipment with current PAT certificates etc, etc - just a small and incomplete selection), together with some pretty strong words around the assumptions that you're making about what they have done, in their 'RP' role. An added complication is that if your business operates throughout the UK, there is different legislation to comply with and you ought to familiarise yourself with each.
I'll cease the doom-mongering - the good news is that though this does need to be taken very seriously (wall and ceiling coverings with poor fire performance have contributed to some of the worst fire tragedies - Google 'Stardust Disco Fire' for an example) - it's not rocket science, There are specialists - some contributors to this forum included - who could help you set these processes and procedures up if you wanted them to (not me - I don't do that any more - I'm quite happy designing buildings)!
Hope this helps - I'm sure others will pipe up with advice, too.
