I also have pretty poor reception with three but they tell me reception is great in my area. I am just going to change when my contract is up. You would probably have fight it in the small claims court if you wanted to end the contract as they won't accept there is a problem.
I have a contract with Three, I live around 80 metres from the river in Rotherhithe, I am often in Tesco at Surrey Quays, and the new one in Jamaica road.
I walk to and from Bermondsey station three days per week.
I am also often in and around Butlers Wharf, Tooley Street, Southwark Street and Union Street, yesterday evening I was at the top of the Shard, and dined in Côte, Hays Galleria after that.
Knock on wood, I've had no service interruptions at all, maybe I'm just fortunate.
Have you upgraded your contract recently? I renewed on T-Mobile earlier in the year and my coverage dropped alarmingly. Apparently the old SIM had problems with the update. They sent me a replacement and all was fine.
The guy in the shop told me this was quite a common problem when people changed their plans.
T-Mobile and Three share masts and they were working on them just before the Bank Holiday so there wasn't any 3G for about 3 days.
I work near Tanner Street Park
I've recently moved from T-Mobile to Three and I get a much better signal and 4G than I ever did with T-Mobile.
It's worth checking the Three coverage map as they show when they are working on the masts.