I seem finally to be fairly close to resolution of my issue.
I made contact with Shaw Gibbs (shawgibbs.com) and spoke to a very informed and helpful young lady called Hannah Jevons, who told me how best to approach this. She did this free-of-charge but did say that should I need further assistance (e.g. when HMRC proved difficult) they would help but their charges would then amount to something in the order of 1,000pds.
https://www.shawgibbs.com/team/hannah-jevons
HMRC allows you to re-submit your tax returns for the last 3 to 4 years (there is a tax year related cutoff date). If you go to their website the forms (SA100) are only available back to FY2014 - but I cut & pasted an old form and used that to submit for FY2013 as well as for 2014-2016.
When re-submitting these, you must NOT complete the Foreign Earnings section - just leave it out completely (at least as far as it refers to receipt of the German State Pension. Obviously if you enjoy other taxable foreign earnings such as property rentals etc they will have to be declared). Refer in your covering letter to the fact that you have deleted the Foreign Earnings sections and give as reason that the German authorities are taxing these payments at source as they are entitled to do under the Double Taxation Agreement Article 14.2.
Within 3 weeks I received a payment of just over 3,000pds - which is actually about 3,500pds less than I expected.
I promptly wrote off again explaining that their payment did not match my calculations; needless to say they had not laid out their calculation in a covering letter. My calculation reasoning was that the 20% tax rate multiplied by each year's German payments must roughly equal the amount I am due (about 6,500pds).
I'm still awaiting a detailed reply regarding how they worked it out and why their payment is less than half of what I expected.
Last point, which may be important point for some: I am now under the UK tax threshold and HMRC have advised that I no longer need to submit Self Assessment forms each year. I now need to inform my bank that I would like my savings paid Gross of UK tax otherwise they will deduct 20% tax.
Hope this proves of some help.