Many years ago I bought a "grey" important 400cc Honda - it had less than 15k miles on the clock - it came with a "warranty" - and low and behold, within a few months there was a problem with the carbs - the rubber diaphragms had perished - not covered by warranty as this was "wear and tear" so into my pocket went my hand, with the assurance that if anything else went on it that it definitely would be covered by the warranty
The perished diaphragms actually let petrol flood through the carbs and into the bores - this then drained into the sump and "raised" the oil level - so while the bike was all shiny and new I was checking the oil and, like you, it looked like the bike wasn't using any oil - so I got out of the habit of checking the oil - with the carb problem fixed the petrol no longer drained into the sump so the real problem of the bike using oil reared it's ugly head - and "bang" went the engine. You've not been checking the oil Mr Voltage - says the garage - not covered by the warranty - - - but, but, but, you said . . .
The ONLY warranty worth having is one you get with a brand new car or bike up to 3(?) years old . . . and even with that the buggers'll try and wriggle out of anything that they can - so a 10 year old car with 200k miles on the clock, costing, I'm guessing <£2k - hate to say this and it's not meant as an insult, but you're "almost" in banger territory, you really are taking a pig 'n' a poke when you buy a car of this age, mileage and price
If the garage is going to source and fit an engine at a cost of £1200 and they want £500 costs towards fitting it then the engine is valued at £700 - you need to find out EXACTLY what they're putting in, cause if it's just a second hand engine that's been power washed you could be chucking good money after bad and then you'll be out of warranty