£100 was a good deal - private sale? - DVLA don't usually sell for less than £250, although that does include fees.
No hassle, I know it takes a while - I did a few transfers 20-odd years ago.
We're about the same age so maybe you remember this:- taking the car to a 'Local Vehicle Licensing Office' (now mostly closed I think) to have the VIN inspected - which often meant parking illegally because they were in town centres with very limited parking (if any) but the staff didn't like to walk far - you had to take the risk.
Then there would still be a few weeks while the paperwork was sorted.
I remember what a revolution it was when you could do a double transfer at one inspection (when replacing one cherished plate with another) - previously it required two visits - so some things have improved - a bit.
I'm amazed the transfer fee has only recently gone up to £105 - it was £80 even in those days - quite a lot of money then!