A couple of thoughts. I can go into more detail on any of these if you need me to.
-When it comes to wireless, there are two ways to plan. One is for coverage, the other is for capacity. Based on the number of devices(capacity) and space(coverage) that you describe, I believe that capacity is going to the be the bigger deciding factor. Remember that wireless is like using an old-school hub. Everyone hears everything. That also means that only one client can talk to one AP at a time. This isn't a limitation of a device (Cisco vs. Netgear) this is a limitation of the physical medium (airspace). Since you are programming for mobile devices, which will only support a single stream, you should plan on 1 dual band AP per 50 devices. If you choose to only support 2.4 or 5Ghz (airspace issues with neighbor offices for instance), then plan on 1 AP per 30 devices.
-The Cisco 887 only has a 100Mb connection. If you keep with your current plan, and do all of your L3 routing on the 887, it will become a bottleneck for anything that routes between your internal networks. Examples include: Local replication for Dropbox, Wireless synching between i-devices and itunes, Copying files from machine A to B, Time machine backups, etc. etc. This bottleneck occurs because anytime data must flow from one network to another (wlan to lan) it will need to be routed, and must go out, and then back in, from the same 100Mb interface. This might not be a big deal, but I wanted to mention it, just-in-case.
-The Wireless controllers are a good idea. The initial setup takes a little while longer, but from that point on, it becomes super easy to deploy more AP's or WLAN's. I don't know anything about them from personal experience, but I have heard good things about the Meraki AP's. It is an cloud-based controller solution, which Cisco recently bought. EDIT for clarity: I don't know anything about the Meraki solution. I know A LOT about the Cisco Wireless Controllers :-).
-How are you powering your AP's? Do you plan on using VOIP in the future? Consider both of these when considering whether or not to order a switch with PoE.
-Also, just noticed, you are planning on putting a firewall in-line after the router. That further complicates your plan to route between subnets there. I would plan on purchasing an L3 switch. That would simplify the deployment considerably.
Hope this helps. Good luck.
The HP can be either a bridge or AP, not both.
I recommend that you do this: just replace the HP with the Netgear, since it can handle more clients than the HP. If your wifi signal is good enough to cover the entire ares, that might be the simplest option.
You also might consider using both: put the Netgear in the same location as the HP. Connect the Netgear wired port to the HP. Use the DHCP server on the HP. Set the HP and Netgear to be on different channels (eg, 1 and 11). You can either use the same SSID or differnt ones, but the idea is that half your clients will connect to the HP and half to the Netgear.
Best Answer
Generally yes, but I suspect not with simple British Telecommunications router.
By using managed switch with VLANs and AP that support VLANs. Or by using AP and Wireless controller that tunneling traffic between them.
Cost of solution can differ depends on chosen equipment. But anyway radio planning and cabling planning is required, specially if You planning to use multiple APs.
UPD. Try to make more specific in project.
1. How many AP is necessary?
One AP can work from 10 to 100 meters, depends on AP, Wi-Fi standard (g ,n ,ac), walls, desired speed, AP antennas and other parameters.
Reinforced concrete make good isolation, so at least 1 AP on floor. One of way is set test AP and try, how far from it phone work acceptable.
2. How many active users must be served simultaneous?
(active mean do something on network or internet)
In 2.4 GHz band only 3 channels simultaneous possible. And more 15-20 active users on single channel in single interference area can make problem with performance.
If it problem meet, use low power AP that have less coverage and less interference area, and possible use directional antennas. But then more AP required. And/OR use 5 GHz band where more channels can be used (8 - 12 depends on country), if enough client devices support it.
If not, You can try use long range higher power AP.
3. Where it must be placed?
There some different solution possible. It somehow like box packaging. Some AP can have directional antennas and make far coverage in one direction and short in other.
It can depend on wiring limitation (maximum 100 meters of twisted pair) and on AP choose.
4. What AP you choose?
Hard question.
For example:
Ubiquiti UniFi is nice, but requite controller (PC software or "UniFi Cloud Key"). And if one or more switch is used it must be VLAN capable managed switch. And there no directional AP that support multiple SSID (if not do reflash to non native firmware).
Mikrotik - any wireless can be controlled AP or work without controller. Any router can be wireless controller (limited only by planned load). More flexible router, for my taste (but less trivial).
Meraki, Ruckus, Aruba ... - can do anything of above and much more, but several times more expensive. And I lack expertise in it.
5. What router to use?
How much traffic must handle the router? (In Your case - What planned speed of internet connection plus estimation of inter-VLAN traffic?)