This page from Kitz
shows what goes on in an Exchange. It's pretty complex as it depends entirely one what tech your using (ADSL has the DSLAMs in the exchange, but FTTC has fibre from the cabinet. It also matters if you have voice from the same ISP as you have data (that's the difference between MPF and SMPF).
With FTTC and FTTP, it pretty much just requires a cable link to the appropriate backhaul (effectively just a patch cable between a switch). With ADSL it's a bit more complex.
In essence there are several products from Openreach used:
1. Line is rented from Openreach
2. A Service Level for the line is bought from Openreach. This ranges from 1 to 4. All consumer lines are SL1 (72 hour clear), most business lines are SL2 (48 hour clear). SL3 (24 hour clear) is hardly used and SL4 is what EFM and EoFTTC use which is 7 hour response time.
3. FTTC capability is bought from Openreach
4. A cable link is bought from Openreach to connect to either BT Wholesale or Talk Talk Business (in most cases). There are other ISPs that run leased lines to exchanges.
5. For consumer grade connections, BTW and TTB offer a highly regulated product that essentially bundles bandwidth for a number of lines. This bandwidth is very expensive, so ISPs contend customers on this backhaul to keep prices down. For 'Ethernet' connections, you can buy this bandwidth directly and have 1:1 contention. Ironically, this bandwidth is MUCH cheaper than the consumer bundle because leased lines are so competitively priced, but as you aren't sharing the bandwidth it's more expensive individually.
6. The backhaul provider also provides the bRAS which controls the lines characteristics and responsible for the IP profile (in BTW terms). This is what you're talking to when you use the BTWholesale speedtest
- however your traffic doesn't go through it, it's more of an orchestration device. bRAS's are a bit shady and not much is known about them or where they are.
7. After the bRAS, you're then finally handed over to the ISP's network who you have the contract with, and they're now responsible for routing your packet through their peering agreements to wherever that traffic needs to go - only at the edge of the core router are you finally on the Intertubes proper.
FTTP is just using a GPON OLT (back to having equipment like a DSLAM in the exchange) which is connected to a fibre that is spliced to all the properties (usually up to 32), which each have an ONT in them. The OLT then just uses a cable link to the backhaul.
A leased line is simpler still by just being a fibre directly to the cable link and on to the backhaul.
All of these are a mix and match of different products between Openreach and the backhaul provider, and you can theoretically pick and mix. In practice, only the LLU ISPs that operate kit in the exchange do this picking and mixing and create a product which is then resold to other ISPs on a wholesale basis.
The key price differentiators are only what backhaul you use, what SL you have. TTB is a bit cheaper than BTW. But for example, an EoFTTC line with TTB 1:1 contention and SL4 costs £75/mth. With BTW it is £5 more at end ISP prices. For consumer grade broadband, the cheapest service I know of is £18/mth which is used as backup line to an Ethernet product.
Therefore you can determine if you're on a BTW backhaul, as the BTWholesale speedtest will test your line. It won't recognise your number if your on another backhaul like TTB.
Although it's highly likely the backhaul is using MPLS, meaning you won't necessarily be able to know what the hops are in a traceroute, they may offer a clue.