Here's where I think you're at with getting better fixed broadband :-
1) Openreach have
cancelled FTTP rollout to your flats (you may not like it but take it as fact as you're not likely to get a signed statement about it from anyone on here).
2) Openreach not likely to upgraded cabinet 109 to FTTC while so few premises connected to it (could change if more premises are connected to it either directly by Openreach or partly/fully funded by developer)
3) Hampshire Superfast are not currently interested in helping, they have made that clear to you.
4) As baby_frogmella has said you and the other flat owners/occupiers could try Hyperoptic.
Hopefully I haven't missed anything out, I am sure someone will let me know.
You have not said what speed your currently getting via ADSL? if its below 10Mb next year at some point you should be able to register with the new Government scheme called USO which aims to provide everyone with at least 10Mb up to a maximum installation cost of around £3,400 per property.
[Edit] You (and the other flat owners) could consider funding it yourselves via a BT community Fibre partnership but FTTC or FTTP won't be cheap.
[Edit] There are a lot of prices floated around for how much it costs to install a DSLAM (FTTC cabinet), if you say the cost was as high as £60,000 (I've also heard people say as low as £30,000) then you would need 18 properties connected to cab 109 (who get below 10Mb) to register with the USO to collectively achieve this figure.
Edited by dect (Sat 09-Feb-19 11:10:29)