That's a disgusting trait....presuming you mean there's no accessible connection point.
Correct - only by lifting a carpet and removing floorboards above. Barely even enough slack on the flex on some of them to remove the lights from the ceiling I suspect.
The correct way would have been a wagolite box or similar above each light so they could be easily replaced...and would have cost maybe a whole £10-15 more.
Instead they accessed where the original lights transformers were from above, and ran the 2 core flylead from each light back to that - including through joists...
Since the flylead from the downlights is 2 core, also no chance of an earth connection in the future if replacing with a Class 1 light without running new cabling.
Maybe they thought if they didn't install new cable it couldn't be blamed on them - what they didn't think was how can I leave a job that the next electrician along will look at and think "not bad", which is the minimum I try to achieve at least!
They did apparently quote for a whole replacement CU at £600+, or an additional sub board for £150ish. The existing one is a mess to be fair and £600 was probably a fair price (except that they'd probably have bunged in a Screwfix Special dual RCD at that price)
Then they moved the existing oven, kitchen sockets and 'lighting' onto the new board - except that the lighting they moved isn't for the lights they installed but for something else that I couldn't identify....
Cracking job all round in other words!