I doubt your first quote was a formal quote. I'm guessing here but it was probably just a figure extracted from a mechanic who gave the bike a cursory look-over and then muttered "chain and cassette." You then asked him how much that was and he thumb-sucked GBP 55. You interpreted that as an amount that will cover all eventualities on the bike. The bike was then booked in and he formally went over all the safety points and added up what needed to be done. My guess is that the bike requires extensive work, is very dirty, hasn't seen new cables, brake pads or bearings since it left the shop new. I also guess that the chainrings are beyond their serviceable life, the cables are so sticky and gritty that he can't make the gears index properly with them and that the wheel bearings and BB require replacement. That quickly adds up. He then evaluated the bike's value vs repairs and quoted you on new, which is probably comparable to the repair costs plus a bit. I doubt he quoted you on a Pinarello Dogma and tried to make his month's quota on one sale.
So, to get to your question: has that happened to me? Yes it has. In ignorance I have on occasion extracted a premature quote from someone on one or other repair and once the job was booked in and on the table, the full picture was revealed.
Don't abandon the shop because you feel cheated. By all means, get another quote but compare apples to apples. Use the repair list your original bike shop has now prepared and get a quote on that. Don't attempt another cursory or telephonic quote without letting the cat out the bag.