There are many discussions about the booster box, Bt Mobile have had two trials of these. Whislt BT own EE they are run as two seperate companies, BT Mobile only uses the network under a MVNO service agreement.
BT are currently testing 4G calling & wi-fi calling, this to me having tried a signal booster box is a much better solution. The booster box has to be connected to your home hub, and allows upto 4 users to use a 3g signal with a limited radious. 4G/Wifi calling allows you to connect to any wifi network in the UK that allows that type of protocol even when away from home.
BT Mobile are clearly working towards this, as it recently started to show text on their website and app but no date for the launch has been confirmed.
If you are unable to wait for wifi calling then maybe it is best that you try another mobile network. I would suggest getting friends on various networks to visit your home at different times of day and see which gives the best coverage.
I've also just moved (mobile number transferred yesterday) because the Tesco Mobile signal was getting worse and worse. Did all the usual coverage checking: 2, 3 and 4G all excellent. Nope. The signal is almost as bad as Tesco's! The person on Live Chat checked coverage. The same result. Even in town I'm lucky if I have two bars. Luckily I am in the cooling-off period and, even with the hassle of changing providers yet again, I'm thinking of cancelling. The package offered by BT was certainly good (apart from the £50 voucher to spend on ridiculously expensive phones!) but the very poor signal isn't worth the aggro.
I've done that - I'm now wondering if it's my somewhat ancient phone - Samsung Galaxy S3 Mini GT-i8190N, although that wouldn't explain the poor coverage for 3G. Even in town (Yeovil) the signal is dropping out: Tesco Mobile was good there. So frustrating and annoying!
If you can get someone with a BT sim or and EE phone and see what their reception is like..
Also as you may have seen, BT have started to migrate sims over for 4G and wi-fi calling, the wi-fi calling will help with indoor coverage, and the extra band that comes with 4G calling (VoLTE) should improve outdoor coverage too.
You never know, BT may even do some offers on handsets for the launch of wifi calling..
I have had exactly the same problem, in fact the longer I get in to this 12month contract the worse the coverage is getting.