Alexander is right. Facts and ideas cannot be subject to copyright, only the expression of them. Since a family tree consists of facts (names, dates. places etc) the contents, wherever they are obtained, are not subject to copyright.
However there is one caveat when it comes to copyright in the UK: Crown copyright.
Crown copyright covers any work made by an 'officer or servant ' of the Crown in the course of their duties, ie civil servants. This means that a compilation such as an enumerator's census return is protected by Crown copyright even though it is essentially made up of facts. In contrast the information in the household census returns we see in 1911 and 1921 is not subject to Crown copyright because the author of the work is the head of the household, not a civil servant.
The other right which sometimes applies is
database right. This can exist to protect the contents of a database, even though those contents may be classed as facts, provided that the database owner has expended "a substantial investment in obtaining, verifying or presenting the contents of the database". Investment in this context refers to financial, human or technical resources. Taking a substantial part of a database can amount to infringement of database right if done without permission. It would not infringe database right to merely extract and reuse a few specific entries which applied to someone you were researching for instance.