With the current travel restriction at the Germany and U.K. border.
Is it possible for a student studying (with a visa) in U.K to travel to Germany (with a Schengen visa) to participate in an internship?
A Schengen Visa is a C-Visa for short term stays. Holders of such a visa are effected by the ban.
Germans, EU citizens and foreigners who have lived in Germany for many years are particularly affected by the regulation. Because people who are neither Germans nor permanently resident here have not been allowed to come to Germany since mid-March because of the corona pandemic anyway unless the have a "valid reason for travel".
Since you are coming from the United Kingdom, the rule that you can transit to return to the United Kingdom does not apply.
So unless you actually have a D-Visa (National Visa) and the trip is considered essential, you probably won't be let in.
An internship would only be possible if the firm is actually working at the moment.
Effective Friday, the 10th of April 2020, most travelers will have to go through a 14 days quarantine.
No quarantine will be ordered for commuters, business travelers and service technicians who have to enter or leave the country for a few days, the decision continues. The same applies to people who would have to transport people, goods and goods across borders, on the road, by rail, by ship or by plane, as well as for travelers in transit on the way to the country of their permanent residence.
Seasonal workers, where quarantine similar conditions exists, will also be allowed.
Anyone wishing to enter for a work stay of several weeks must be able to demonstrate that a two-week quarantine is ensured or that equivalent operational hygiene measures and precautions to avoid contact apply. This is intended to enable seasonal workers, especially in agriculture, to work in Germany.
- 14 Tage Quarantäne für Einreisende (in German)
Since you are a student in the U.K., I assume you have at least a long-term visa for the U.K. In this case,
you are allowed to travel through Germany to reach your home country if no other travel connection is possible.
Entry for purposes of tourism is no longer allowed.