I had the same problems right after upgrading to 7.1. I have done everything suggested , even completely restored to factory defaults my iPad air and set it up as a new device and o apps and still had the same issue. Then I found out some blogs talking about old issue where routers QOS ANS WMM settings on your router impact the speed on iOS devices.
I didn't believe it as I still had two other iOS devices running 7.04 and not having any issues. I have followed the instructions and located the WMM setting on my router and after disabling it my iPad air running 7.1 is getting 25mb / sec speeds again.
The WMM setting is a wireless setting and entailed by default on the router. You will have to login to you router via 192.168.1.1 page and locate the wires settings and look for something called WMM setting and disable it. Each router is different so you will have do the research on your router. I have Model Belkin Play Max / N600 HD (F7D4301/F7D8301) v1 running tomatoe firmware. If anybody needs exact steps for this router let me know otherwise just google your router name and WMM setting to find exact steps in disabling it.
This worked for me but believe me when I say when the iPad air was running 2mb/sec and pages were loading so slow, I was very upset with apple. Now I don't know what to think since it's not like apple can control our local routers setup.
Another suggestion I might have is to take your device to friends house and try on a different wifi to see how it reacts to different environment. Or take it to Meijer or any place that has free wifi access. Once you see that the device can run at high speeds you will believe a simple setting on your router can somehow impact the device function.
Good luck.