1) Is this possible?
Generally yes, but I suspect not with simple British Telecommunications router.
2) How do I make it so the server and the desk are only accessible by
their respective networks?
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?
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?)