Depends, the German treaty is more complicated that others when it comes to the pension.
Default position is it's taxed in country of residence only, so in your case: UK
That is unless you satisfy sub para 3 which can get messy, in which case it would be taxable only in Germany.
Would need a lot more info to comment.
With regards to your consulting income, need a lot more info. But yes, it's fully taxable in the UK as you are resident here, but if any of the profits are attributable to a PE in Germany, then that portion is taxable in Germany first with a credit availabe in the UK for the German tax payable.
As you are physically present in the UK for the full year, what activities are being performed in Germany that would constitute a permanent establishment?
Relevant earnings is effectively 'earned' income that is taxable in the UK (so not passive income such as rental, interest, dividends, etc). So yes, your consulting income would likely be consdiered relavent earnings.
Overapaid tax in Germany, you'd likely be able to file a German return or such to reclaim the overpayment.
Paragraph 3 states:
"3) Notwithstanding the provisions of paragraph 1, such a pension, similar remuneration or annuity arising in a Contracting State which is attributable in whole or in part to contributions which, for more than 15 years in that State,
a) did not form part of the taxable income from employment, or
b) were tax-deductible, or
c) were tax-relieved in some other way
shall be taxable only in that State. "
The point is that the pension (or rather early retirement payment) I am now receiving was contribution free, rather it was a contractual right i.e. therefore, for all intents and purposes, the contributions did not form part of taxable income (because there were none!)