Interesting that on Youtube the video is titled collapsed rest bend, which is just below ground under the cast iron stack pipe with the hole cut in for the camera.
That's not £13000 worth probably not even if they propose repalacing all the pipe to the main drain, reconcreting driveways and paths etc
** I'd written all the below before I spotted the note on Y-tube. **
There's no way based purely on that video that the cost to repair is £13000.
At best that's a guestimate from a drains cleaning company who would sub the works to a ground worker, you need quotes from people who replace drains, not clean them.
How much has the intitial visit / camera survey cost and has the blockage been cleared, even if temporary?
Did he locate and mark the route / depth of the pipe to see what obstacles at ground level there would be for digging up, like the garage and greenhouse seen in the first few frames?
The final frames of the video indicate the camera is swinging side to side suggesting that section is vertical and may be looking down into a common drain which would be the responsibility of the local water company if they're saying the problem is down there.
If he or anyone else mentions putting a liner in, refuse it and ask for pipe replacement, unless liners are fitted by someone who is very experienced, they fail and cause more blockages than the original problem and you'll end up paying to have all the liner removed and replacement pipe fitted.
Not all pipe repairs are suitable for relining.
From the video there do appear to be some misaligned / bad pipe joints but no collapses and nothing too serious
If the drain is clear and running it may be worth leaving it untill / if it blocks again and look at options then.
