Thanks Axo, I'll probably just buy a new hard drive instead to save the trouble. If I back up my whole MacHD onto an external HD and then delete content off my MacHD, when Time Machine next backs up my external HD will it erase the content I erased and copy my current MacHD?
Recommendation:
Step 1: Buy the biggest external hard drive that is sensibly priced. For example, right now I can get 2TB for £60, 3TB for £75, so I would buy 3TB. Make sure that hard drive has no fancy features. If it says "Mac compatible" you just pay extra (all hard drives are Mac compatible). If it says "Backup" in the hard drive name, you just pay extra for backup software that is going to interfere with Time Machine. Yes, if you want a hard drive to backup your Mac, avoid one that says "Mac" or "Backup" in its name.
Step 2. Backup your Mac to the Time Machine drive. So now you have all the files twice, in case of some disaster, and everything is safe.
Step 3: Move whatever files you want to move to your old external drive, and back it up as well. Only then delete the old files on your Mac.
Initial Time Machine backups take ages. Don't worry about that. You can use your Mac while the Time Machine backup is running.
If you are worried that thieves could steal your backup drive and get all your data, Time Machine lets you encrypt the backup drive. It makes no difference to the operation except that you have to enter the password for the backup drive sometimes.