iOS Update

Try this, see the following Apple articles:

Update your iPhone, iPad, or iPod touch

Update your iPhone, iPad, or iPod touch - Apple Support (IN)

If your iPhone, iPad or iPod touch won’t update

If your iPhone, iPad, or iPod touch won't update - Apple Support

You can do the update via PC, see this Apple article: Update software on iPhone, iPad or iPod touch in iTunes on PC

Update software on iPhone, iPad or iPod touch in iTunes on PC – Apple Support (UK)

If you have a Mac see this Apple article: Update your iPhone, iPad, or iPod touch with the Finder

Update your iPhone, iPad, or iPod touch with the Finder - Apple Support

You need about 6 GB device storage and good Service & Wi-Fi.

If they are On, turn Off Hotspot & VPN.

In addition to this I’ve had a “non genuine” battery installed but I can’t see how this would prevent iOS updates.

Not sure, if that would prevent iOS updates.

Although it may appear obvious, rebooting your iPhone can often resolve update issues. Hold down the power button on your iPhone until the "Slide to Power Off" slider appears. If your iPhone lacks a Home button, press and hold both the side and volume buttons at the same time.

Make Sure Your iPhone Has An Internet Connection

To download new iOS updates, your iPhone must be connected to the internet. Some updates, due to their size, necessitate the use of a Wi-Fi connection.

Make Sure You Have Enough Free Space

Check to see if your iPhone has enough space to store the update. iOS updates typically require 750-800 megabytes of free space before installation.

If iTunes Doesn’t Work, Try The Settings App (and Vice-Versa)

You can update an iOS device in two ways: through your computer (iTunes or Finder) or through the Settings app. If you're having problems updating your iPhone using iTunes or Finder, try the Settings app. If the Settings app does not work, use your computer instead.

Updating Your iPhone In iTunes

1. Open iTunes on your computer and plug in your iPhone using your Lightning cable (the cable you use to charge your iPhone).
2. Click the iPhone button at the top of the iTunes window.
3. Click the Update button on the right-hand side of the screen.
4. Confirm that you want to update your iPhone by tapping Download and Update.

Updating Your iPhone In Finder

When updating your iPhone on a Mac running macOS Catalina 10.15 or later, you'll use Finder rather than iTunes.

1. Connect your iPhone to your Mac using a Lightning cable.
2. Open Finder.
3. Click on your iPhone under Locations.
4. Click Check for Update.

Is Your iPhone Compatible With The New Update?

Every year, a few older iPhones become incompatible with new iOS updates. It's possible that your iPhone will not update because it's incompatible with the new version.

Visit Apple's website to see a complete list of iPhones that can download and install the most recent iOS update.

My iPhone Still Won’t Update!

If your iPhone still won't update, you'll need to restore it in iTunes. Before restoring, make sure you have a backup of your phone because you will be erasing all content and settings from your iPhone.

Know the features and security fixes done by Apple in iOS 15.6.1

Ollie ~ You should expect such issues, as Apple states: "Using nongenuine batteries might also result in unexpected behavior after installation, device software updates, or while charging. Using nongenuine batteries might also lead to safety issues." Source:

About genuine iPhone batteries

...Have the battery replaced:

iPhone Battery & Power Repair

Repair Provider Verification - Official Apple Support

...Found by searching Apple's Knowledge Base.

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Ollie-Blaize wrote: "Yes I know I can’t access “battery life” but this shouldn’t impede the ability to update an iPhone."

Ollie ~ Aren't you concerned about the safety of those around you?...

"These genuine Apple batteries have also been certified for safety."

"...using nongenuine parts might affect the safety of the device..."

"Using nongenuine batteries might also lead to safety issues."

Source: About genuine iPhone batteries

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In addition to this I’ve had a “non genuine” battery installed but I can’t see how this would prevent iOS updates.

Before a new update is applied, the software checks the Battery Health on your phone along with some other things. Not sure if you noticed before, but "Battery Health" on your phone will not work correctly because a non-genuine battery was installed on your phone.

Because the replacement battery does not allow Battery Health to function correctly, the update cannot proceed.

If you want the update, you'll need to have a genuine Apple battery installed at the Apple Store or at an authorized Apple Service shop.

You do understand that the after market battery took away an important feature and function with your iPhone, correct?