i would say one extra thing you need to consider there..

One possible cause..

Home Plugs!!! OMG etc..

They use the same modulation scheme and bands as ADSL/VDSL and if your neighbour has them then their mains radiates the noise and some may even get back out to the pole and back to you direct if you are on the same circuit.

If you have them yourselves then turn em off and see what changes..

Otherwise whatever the interferer is, there is probably nothing Openreach can do about it. This is the nature of unscreened open twisted pair lines ..

ADSL is covered by CE accreditation and BT has several demos of kit it has recovered that was offending in terms of errant RF emissions.

Odd you mention them, as yes have tried with and without with no adverse effects.

Perhaps not all home plugs are created equally,

This thread is getting odd, you seem to be asking questions that you know the answer to.

I'm guessing the OP has read a little, and has thrown a few gleaned terms in their posts.

SFI engineers from Openreach(cough.REIN trained engineers surely) have in the past found interference sources that may be 100m or more away from a property, i.e. they are able to identify sources given the time to investigate.

We go much further than that.

In reply to a post by kijoma:

Otherwise whatever the interferer is, there is probably nothing Openreach can do about it. This is the nature of unscreened open twisted pair lines ..

Well, they could stop relying on such antiquated technology for broadband connections!

To answer the original question, surely the answer is an absolute no. Sunspots themselves are just areas of cooler stuff on the sun - they themselves are 93 million miles away from any ADSL connection. A side product of sunspots (and some other things on the sun) is solar storms that produce xray radiation storms which interact with the upper ionosphere of the earth and hence have an affect on radio propagation (but still several hundred miles from any ADSL) and CMEs which interact with the earth's magnetic poles and also upset the ionosphere. A severe solar storm can induce dc currents in long wires on earth such as power distribution networks.
ADSL is carried by balanced cables, any dc coupling will not affect the differential ADSL signal.
At the moment and for the next few (or even many years) the sun is approaching the next solar minimum. Sunspots are rapidly disappearing and the chances of something like the Carrington storm of many years ago is practically zero.