Currently Apple doesn’t allow users to switch from the default Safari browser on an iPhone, iPad, or iPod.

One suggestion I found while researching this, is to share the links from Safari to the browser of your choice.

Using VoiceOver for accessibility, when you have gone to the web site you choose to visit in the Safari browser, perform a four finger single tap at the bottom of the screen. Then swipe right to left to move back to the “Share” button and one finger double tap. Then swipe left to right from the top, and on the first button labeled “More” perform a one finger double tap.

The list that comes up will have whichever browsers installed on your device listed, perform a one finger double tap on the ones you whish to use, which adds them to the share list.
You can then choose the browser to open your link, however you need to do this for each and every web site you visit.

I personally chose Firefox, Chrome and Opra Touch as my browsers; which allwork much better than Safari.