Looking on street view, the exchange is just past St Mary's church on London Road. There is a cabinet outside the exchange but no number visible, there is also a cabinet on London Road on the opposite side to the junction with Sanderling Way, again no number visible.
That's about the right distance for your expected ADSL speed. How far from the cabinet are you, if the cabinet is between you and the exchange I don't understand why the checker isn't showing some level of VDSL capability.
Absolutely, even at 1300M there should be a reasonable figure for VDSL.
What does the checker show if you enter your full address rather than phone number?
I think the best thing to do is speak to customer services and get them to raise an ORDI (Openreach database integrity) request with Openreach.
I doubt you will get G.fast at that distance from the cab but you should get around 60M VDSL.