You say that you have connected at many other places, and receive high download speeds there? This would suggest that there isn't an issue with the iPhone itself, since it is clearly able to run high speed WiFi, but instead an issue with your own internet. I would recommend connecting another device to the same network, perhaps a laptop or another mobile phone, and testing whether they receive similar speeds. If you have the same issue on all devices, I would recommend contacting your internet service provider (ISP), and inquiring them.
If the issue is an isolated one, and only occurs on your iPhone, first make sure that you are on the latest version of iOS. Then, I would recommend reseting network settings. Go to Settings > General > Reset > Reset Network Settings. This also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you've used before. Reconnect to your network again, and see if the issue still persists. If it does, then I suggest contacting Apple Support (remote diagnostics and/or mail-in service may be available, if required), making a Genius Bar reservation or visiting an Apple Authorised Service Provider for assistance:
- US: iPhone Service Answer Center - Apple Support
- Elsewhere: Apple - Support