Welcome to this user forum.
Most disconnections are cause by line noise or high resistance connections.
Is there any noise on your phone calls? Dial 17070 and select option 2, there should be no noise between the announcements.
If the home hub lights are not changing colour when you get the disconnects, then it may simply be an issue with the home hub.
With so many smart devices, you may be better using your own router instead of the basic home hub, as wireless issue with the home hub seem quite common.
The BT shop has a number of product for a connected home, but I am not sure how effective they are.
I would try a factory reset of the home hub first.
It sound like a similar issue to the one my daughter had in her house, when using a home hub 6.
I changed the router for a third party one costing about £40, and the wireless disconnection issues stopped. That may be worth a try.
Wireless extenders are a waste of time and money, and they can make the problem worse.
This post may be of interest https://community.bt.com/t5/Home-setup-Wi-Fi-network/Faulty-smarthub-6-wired-and-WiFi-problems/m-p/1...
before buying a 3rd party router it would help whichever router you have for the master socket to be more central in your home rather than in an extension Openreach may be expensive to make the change of position but you could try a local telecom engineer who would be cheaper
with the hub have you split the networks http://bt.custhelp.com/app/answers/detail/a_id/56419/~/how-do-i-split-my-bt-hubs-ssid-%28wireless-ne...
have you tried changing the wireless channel from auto to a fixed channel both 2.4/5ghz
I use a hh6 and compared it against a Tplink VR2600 with 4 external aerials and in my home the hub gave better overall coverage than the then top of range tplink
if you already have FTTC then moving ISP will just be the same connection but different router as it is openreach engineers for all ISPs apart from virgin then it will be self instal with no engineer visit
If its an issue with the line, then changing providers will not help, as it will still be the same pair of wires that they use.
My personal opinion, based on other reports on this forum regarding smart devices, is that is a home hub issue.
Trying a different router would prove what the issue is. You can get a TP-Link TD-W9970 locally if you are near a main town. They cost about £40 (Argos) or less, and most places will allow you to return it if it does not fix the problem.
Reports from other forum members, have confirmed that it solves the wireless disconnect issue.
Is going to be a lot less hassle than changing provider, and the possible loss of service that would incur.
See Technical Glossary - Look here for an explanation of broadband terms.
ISP = Internet Service Provider.
FTTC= Fibre To The Cabinet.
You seem to have manged to setup all your smart devices, so you must have a bit of knowledge.
Personally, I cannot see the point of smart devices, but its probably down to my age. I like a simple on/off switch, works 100% of the time