Welcome to this BT Retail forum. @Littlelou
Its Openreach that provide the external network not BT Retail.
This page should help https://www.homeandbusiness.openreach.co.uk/fibre-broadband/when-can-i-get-fibre
The other alternative would be https://communityfibre.openreach.co.uk/
if you are talking about adsl broadband and not fibre then it is distance form the exchange that limits your speed not the distance form the cabinet
In our area we are all mobile broadband as land broadband isnt working 0.7 mbps all the companies have quoted 1-3 mbps, again go a mile up road to a different postcode but the same cabinet it provides 20mbps.
Do you have a working phone line with BT Retail?
People don't generally use sites when they don't need them, at least that's what I find so I don't often use this site - in fact I haven't used it for at least a couple of years but you might find it useful. I saw your post and don't like the idea od our squaddies not "treated proper" especially in terms of essential services such as communications.
Anyway at the risk of being told off for posting a link use the thinkbroadband site for comparisons, although there aren't many in there for your area at the moment which (as I said before) would mean folks are either happy or happy to understand they can't do much about their situation.
This is the result for your geographical area (not by postcode but by map) https://labs.thinkbroadband.com/local/index.php?tab=2&election=1#15/51.9018/-2.2195/test/exchanges/ using two criteria, speed and exchange
Mobile broadband is fine as long as you aren't going to be frying your heads, your children's head, your friends and neighbours heads with 5G frequency use. It does fry heads, bodies, organs (all organs) and I will not be happy if it comes to my area on my street furniture or anywhere near me. In fact my neighbours and local councillor have bought catapults just in case they try it.
Someone in your area is getting good throughput as can be seen on the test results (well not spectacular admittedly but not bad)
Can't you guys get together and go to your pursar or accomodation officer and ask that landlines with good throughput are installed ? Hpw many are there of you who could take advantage of good broadband (you didn't say if you were in married quarters... something else which might help?)
Just nag and nag and nag and you tell them you HAVE to have something approaching decent. You are protecting us from foreign harm after all.