Welcome To The Cuckoo Community @John Warburton.
Well that was a great read and i like your honesty 
And keeping good company with the business owner downstairs
so i love this community spirit which seems lost in many places these days.
First Let Me Start by saying that from what you’ve stated you have a Standard DSL Connection with speeds like that and not a Fibre (FTTC) Connection From Your Nearest Connection Point,You did mention that SKY & BT Offer Fibre so there shouldn’t be any issue with you having your own connection installed seperately as all lines are Owned/Operated by OpenReach and the Internet Provider Just Rents It.
If you would like The Cuckoo Team to run a check on the Connection points in your
area then please Dont Hesitate To email your details across to hello@cuckoo.co and
someone will get back to you within Working Hours with a potential Speed Estimate.
If Your Interested Then Please Do Register for Early Access as theres Some Codes
Going Out Next Week.
However as The Community is always Open someone will be around to help out.
You can also run your own check using the Offical DSL/Connection Checker Below and it will show you what products are available or not…Most Providers use this for checks but they also have different systems this one is just simpler for the End User (Customers/Us).
https://www.broadbandchecker.btwholesale.com/
Pop your details into this page above and it will show you what your connection point can offer down a OpenReach Line and if you dont have one this can be arranged but there will be a charge for the New Line install which can be given to you on the email address or if one of the team replys here.
Its always best to have your own line rather than a “Shared” line and most connection points
can have a minimum of two lines installed for a domestic property with others added if needed.
So basically if Fibre Is Available Then Yes Cuckoo should be able to Supply You…but it will depend on the Cabinets Speeds/Pole nearest you and with only a 1 month only rolling contract your Not Tied In like most providers.
The Cuckoo Router Specs are Below from a third party website but should give you the details you need its not a cheep (see what i did there) Moddm/Router like other providers use.
https://www.broadbandbuyer.com/products/35557-technicolor-dwa0120/specifications/
ISP’S Do get you to use there tech as its there own Hardware and model they are trained to understand and not any third party routers like your other setup you mentioned so they cant advise or control your own hardware thats why they got you to check with there own equipment.
Most Modern Modem/Routers Do Support IPV6 but im a IPV4 Fan but im not sure if many providers offer this at present as its still early days.
I do like Your SSID Name Though. 
Also It Sounds like there is Blocked Ports/Options in there Router to restrict your setup from functioning correctly but there should be an option to override the DHCP And Input Your Static IP Details ?? So it might be worth looking through there routers advanced settings from its login pages.
Cuckoo Do Agree that Broadband Is Broken and this is why they want to change things.
Thanks For Getting To The End Of My Ramble If You Got This Far.