XPS 15 9550 Instantly Turning Off When Bumped or Right Arrow Key is Pressed.

Using it on the desk =
does the issue happen when only on battery, no AC adapter?
does the issue happen when the battery is removed from the laptop and only using the AC adapter?

Yes issue still happens in both scenarios

Yes, I have tried removing and booting the laptop without the SSD, RAM and Wireless Card in, problem still remains. I was even able to bump the laptop when the back cover was removed which caused the laptop to switch off. I also checked the DC jack cable was connected properly. All internal components look to be fine but i was unable to remove the heat sink (don't want to damage it) in order to check the keyboard and motherboard.

When you had the bottom cover removed to uninstall the battery, did you visually check all areas to see if any component was misaligned causing it to "press" against the inside of the bottom cover?

I believe the issue may have been caused by a bulging battery i experienced when on a flight to Dubai recently. The trackpad became unclickable while on the plane as the battery had expanded and was pushing it out of its socket. I was only watching a film stored on the hard drive on my laptop but once i had noticed the problem i immediately switched off the device. On arrival to Dubai, the laptop battery had gone back to its original size but this is when i first noticed the problem of any movement on a soft surface causing it to shut off.

Unfortunately however the laptop is nearly 3 months out of warranty and this is looking like an expensive repair to a £1200 laptop that is just over a year old, when there was nothing i could do about the fault with the laptop

The laptop will need to be returned to the Dell Repair Depot so that they can try to replicate the issues and replace parts. They should send you a box and return waybill. Attach a detailed note to the laptop so explaining how/when the battery bulged and the issue it has caused.