@PaulieP 

Hey Paul

Hopefully some tof these answers will help!  

First off I would recommend going for the AP225v3  and not the 115    -  The 115 is nearly if not end of life, the EAP225 would serve you better for longer.

Can I switch off wifi on the router and remove the anennae? 

Yes you can indeed and its likely recommended you do this when running alongside APs.    You dont need to remove the aerials unless you wnat too, disbling the radio should suffice

I was looking at this PoE switch ... TL-SG1008P V4 ... will this be adequate?

That will work fine so yes, however you may want to consider going down the SDN route and adding a controller...  if so look at the TL-SG2008P   

Is there one piece of equipment that can do the work of both the router and the PoE switch?

Not for POE device no.. what you have is the best option

I have also seen talk of a controller ... do I need one as well as the router and switch? (I am not sure what a controller does)

In basic terms, the controller allows you to better manage the 3x APs and switch (2008P).  It will 'control' the network better and allow you to do more advanced settings, routing etc.  The big selling point for you would be it can manage your APs better from one central point.   You are then configuring one network as a whole, rather than 3x individual APS.  

The controller will also decide when to move a device/client from one AP to another therefore somewhat taking it out of the clients hands.. clients dont like roaming until the very last resort when signal is dead.   It will also move channels on the APs to avoid interference and provide you pretty graphs/stats etc :)

A controller is what is says, a controller / automatic administrator for the switches and APs.   If you can afford the £50 i would recommend getting an OC200 to manage the APs personally

@Philbert Thank you very much for your advice and explanations. 
All makes sense now you have laid it all out.
I feel more confident in going ahead with this now  

@PaulieP 

Not a problem, glad to be of help!

Suprised you could actually make sense of my ramblings; I kept getting distracted earlier when replying to you and re-reading it now, well its a bit random! lol 

But if you have any queries at all or want to blue sky an idea, dont be afraid to reply. 

best of luck

Phil