From your photographs:
*The ground level at the rear of your house appears to be lower than the front of the house, so assume the house is on a hill sloping down to the garden. There is the appearance of re-mortaring of the brickwork which looks to be London Stock brick, ubiquitous around the capital's turn of the century properties.
*Possibly there was an side door or window, since bricked up. Can see the surface floor height of the suspended floor through the french window at the rear.
*Also noticable is the green algae on the side of the rendering close to where the smell is as indicated on diagram. This may be a "over-time" issue of water/waste pooling towards the area where the side return (concreted) surface area is abuts with the patio area with granite like slab surface.
That green algae type growth has not appeared overnight. When the patio was constructed the draining aspect of it would have been very important.
*I'm sure there is, but I can't see it, a damp-proof course within this area of the building. I trust the patio work has not "bridged" the damp proof course, but difficult to tell from photos.
*The unblocking will have no doubt helped, but the noticeable smell following it may be a lingering one released from the freeing up of the blocked pipe. The improved drainage and ventilation might make this vanish over time. However, I would have expected to see MORE ventilation bricks, as you have quite a significant area of suspended ground floor. They must be plentiful and not blocked.
*The fact that the drain expert saw the incorrect smaller pipe coupled into the T-junction which had a connection sleeve designed for a larger diameter pipe is of quite a concern. Clearly, any waste could flow around the small (undersized) pipe aperture as it is loosely fitting at the connection point. The drain expert is absolutely right to point out this poor workmanship, and this could have been like this for years - hence the green algae build up and likely development of a pong as it has pooled to the point of the waste build-up being so great, and such a "pile" that you notice the smell.
*Perhaps speak with the expert at length again, as I fear you should have this remedial work undertaken. There will be disruption and cost to you and your family. That side return to your property and where its abuts the patio will need to come up to attend to the cracked pipes and incorrect fittings.
*Prior to you having bought this property the previous owners had the work done. It will be difficult to find any guarantees etc, etc. They may have not been very decent professionals who did the work. Did your survey pick up on anything even remotely commenting on it?
*It may well be that you have to "take a hit" on this situation but it will be worth doing in the long run. Again speak to the expert, and get quotes from others too. You need to find out what is involved externally, and internally, i.e. is it a case of skirting boards off, floors up, underfloor heating (either wet (plumbed) or dry (electric) being replaced?
Every situation like this can be fixed, at cost and faff, and be returned to looking like new afterwards. It would best be a spring/summer job, which could give you time to look carefully at what's involved and finance it, or indeed potentially an insurance claim, if you can bear it!
But this is of course only my keyboard and me. I would recommend expert intervention from reputable firms. Some damp proofing companies may also be able to help with drainage, as well as outright draining experts. (Look out for accreditations that companies can attain, which helps to pick off the cowboys from the miriads of firms out there - having a sticker that says Master Builder on the back doesn't cut it).
Your situation needs to be "accepted" as one that isn't going to go away on its own, so you need to brace yourselves and do your research. Of course, flats have problems too, so don't let this put you off being a house owner. Soz for long ramble. All the best with it X