Hello ianfrombath,
When you're trying to download your apps, make sure you're following these steps when you're using Assistive Touch: Use AssistiveTouch on iPhone - Apple Support.
Use AssistiveTouch
Tap the menu button, then choose an action or gesture.
For a multifinger gesture, do the following:
• Pinch: Tap Custom, then tap Pinch. When the pinch circles appear, touch anywhere on the screen to move the pinch circles, then drag them in or out to perform a pinch gesture. When you finish, tap the menu button.
• Multifinger swipe or drag: Tap Device > More > Gestures, then tap the number of digits needed for the gesture. When the circles appear on the screen, swipe or drag in the direction required by the gesture. When you finish, tap the menu button.
To return to the previous menu, tap the arrow in the center of the menu. To exit the menu without performing a gesture: Tap anywhere outside the menu.
If you're following these steps when using Assistive Touch and you still have an issue, please explain more about the issue and behavior you're encountering. If you see an error when you try to install an app, include the error message. This page can also offer further assistance and guidance for using Assistive Touch: Use AssistiveTouch on your iPhone, iPad, or iPod touch - Apple Support.
Additionally, you may want to check out the information on this page to learn more about getting apps installed on your device and what to do if you cannot install any apps: If you can’t download or update apps on your iPhone or iPad - Apple Support. There's some suggested steps here that can help with resolving issues with installing apps to your iPhone.
We hope this information helps you out.
Cheers!