Update November 2018: Please note that Brexit will bring significant and currently unforseeable changes in this field
The below text explains the legal situation pre-Brexit:
If a German debtor refuses to pay the first issue to clarify is whether you must sue him in Germany or whether you can sue in the UK. In other words: It must be resolved which country’s courts have jurisdiction and which law shall apply. The parties may have agreed on these issues in the contract (however, such clauses may be void if used vis-a-vis a consumer). If the contract does not comment on the issue of jurisdiction then the EC regulation n° 44/2001/EC must be applied (COUNCIL REGULATION (EC) No 44/2001 of 22 December 2000 on jurisdiction and the recognition and enforcement of judgments in civil and commercial matters). As a rule of thumb: German courts are competent if defendant is resident in Germany or if the place of performance is Germany. How to make a court claim in Germany is explained here.
In case the German debtor can be sued in the UK then the resulting judgement must still be enforced in Germany (unless the debtor has assets within the UK). Money judgments and authentic instruments of other EU states, including the UK and Ireland, are recognised in Germany. This is, since 1st of March 2002, established by the same EU-Regulation n° 44/2001/EC. Older judgements (i.e. titles issued before March 2002) may still be recognised under the former Brussels Convention. Thus, the claimant does not have to repeat court action but he must simply send a request for enforcement to the High Court (“Landgericht”) where the defendant resides. Together with the request he must produce certain documents, inter alia a copy as well as a translation of the UK judgment and a certificate according to art. 54 of regulation n° 44/2001/EC. The decision of the German Landgericht will be served to the defendant and the claimant may start execution procedures immedately after he is in possession of the so called enforcement order.
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For more information on the German legal system: the bilingual brochures “Law – Made in Germany” (free download here) as well as “Continental Law” (free download here), published by the German Law Societies explain the basic principles of Continental Law. If you wish to look up specific German legislation you find central German statutes on the website of the German Department of Justice (here), including an English version of the Code of Civil Procedure. The German Civil Code (Bürgerliches Gesetzbuch) is available for download here: German_Civil_Code_in_English_language.