Upvote:3
Not sure what can or cannot be done but you can always apply. If the consulate cannot issue a visa for a technical reason like that, they should decline to process the application, which means you would get back your visa fee and the documents you submitted. In principle, they should also tell you that quickly. There is no risk of an actual visa refusal, with all its unpleasant consequences.
Unfortunately, because the German consulate in London uses a third-party outsourcing company to handle visa applications, there is apparently a non-refundable GBP 15 service charge on top of the visa fee and it might be more difficult to get competent advice for a special case like yours.