As Alavahalf suggests, consider another network which uses different transmitter masts.
Avoid GiffGaff, Sky Mobile and LycaMobile, as they all use O2's masts (as Tesco Mobile does).
These providers use EE's masts: BT Mobile, Plusnet Mobile, Utility Warehouse, 1p Mobile and The Phone Coop.
These use Three's masts: iD Mobile, Smarty and FreedomPop
These use Vodafone: Voxi, Lebara Mobile and Talkmobile.
Asda currently uses EE's mast but is about to change to Vodafone.
Virgin Mobile is also in the process of switching users from EE to Vodafone.