Claim
You are allowed to register to vote twice—once at home and once at university.
A screenshot of a tweet by science writer Dr Ben Goldacre claiming that students can register to vote at two addresses has been shared hundreds of times on Facebook.
This is correct. It is possible to register to vote at two addresses if, for example, you are a student with different home and term-time addresses.
In a general election , you can only vote in one of the places where you are registered to vote. As that is one election, you are only allowed one vote. But, as the post correctly says, you can choose which of the two areas to vote in, and can make that decision on election day.
In local elections you are allowed to vote in both areas—provided they are not in the same local authority—because each local authority vote is counted as a separate election.
Conclusion
Correct.