Hi and welcome to the forum.
I'm 1.8km from the cabinet, rural.
From your previous ADSL speeds, pre fault, you are obviously on a long line, of course on ADSL service it's total line length to exchange which will determine your max attainable speed.
From the BTw BB checker data you have provided it looks very much like your residence is also a long way from the DSLAM (fibre cabinet) judging from the relativly low DS/US speed predictions for VDSL (FTTC) service.
Regarding any possible, still existing line faults, I would have thought that the line from PCP cabinet (your local connection point) to your residence would be more likely to be suspect than the line from PCP to exchange, this of course would still be a major factor regarding VDSL service, very likely more so than with ADSL service due to the higher frequencies used should you decide to migrate to VDSL provision.
I believe John Lewis BB provision is under Plusnet?
Not sure what modem/router John Lewis currently provide?
If this is a Broadcom chip based device such as ZyXEL is there a possibility of obtaining any line stat's for analysis?
Various method to achieve this are readily available on many areas of this forum and there are many very knowledgable patrons here who can advise on the modem stat's produced.
If/when the line fault is sorted you
should achieve much better line speeds than ADSL with FTTC VDSL service, of course, due to line length, there is no expectation of your line ever achieving close to the max FTTC 80/20 standard.
As "g3uiss" has posted, a very bad and/or very long line can certainly produce worse results on VDSL than ADSL, every line is unique, for my money I would give it a try if/when the fault/s are sorted and you are back to stable ADSL service.