https://www.parts-people.com/index.php?action=category&id=151&subid=904&refine=battery

Swollen batteries were found on all computer manufacturers' models awhile back. Today's batteries can swell when reaching end of life. It's dangerous to leave the bad battery in the laptop. Remove it and try using the adapter alone. You might not find a genuine Dell replacement for your laptop. Don't buy from private sellers on marketplaces. Lots of scams with batteries. If it works on the adapter alone use it as a desktop replacement until you can buy a new computer. See this for an explanation--

https://www.dell.com/support/article/en-us/sln128667/dell-laptop-battery-frequently-asked-questions?lang=en

I live in the UK. Do you know where I can get a replacement battery? Dell does not seem to sell them and most of the web links I found are not genuine.

During a search I see places claiming to sell genuine batteries. I don't know about UK sales but hopefully you can find one. My last laptop manufacturer wanted $300 to replace a battery on a 6 year old laptop and simply wouldn't sell it to me to install.

I just removed the battery (turn it in somewhere that properly disposes of them.) and used it as a desktop as suggested above. I couldn't find a genuine battery. That was from a manufacturer that couldn't even provide decent communications in English though.

I purchased an American brand this time around hoping for better support. I hope that you're able to find a solution to your battery woes. I also hope when mine goes bad I can find one for mine...

Can I just unplug battery cable from inside the laptop without having to remove it all? Or do I HAVE to remove it ? 

It'll continue to swell until it destroys the chassis, mainboard or other components - or vents and possibly catches fire.  ANY swollen battery needs to be removed and disposed of ASAP.