The making of a copy of a work, other than a computer program, by an individual does not infringe copyright in the work...
There are restrictions - it must be for the personal use of the person making the copy, who can't gain commercially from it, and they must own the original from which the copy was made. But making back-up copies and copies in different formats are all legitimate now.
This means that you can legally convert CDs to MP3 files for your own collection, or put them on iTunes or Google Play. Converting your own LPs into MP3 files or burning them to a CD is also now officially legitimate. You can make your own compilations to listen to in the car. In principle, if you wish to make an electronic version of a book to study on a computer, this is also okay.
However, the law doesn't permit the giving or receiving of mix tapes or mix CDs - a copy would be going to a person who doesn't own the original.
An interesting question
There's a section that follows the regulations, with the heading:
Remedy where restrictive measures prevent or restrict personal copying
As far as I can tell, this argues that, if a copyright owner has in place a mechanism to prevent someone from making personal copies, this person can complain to the Secretary of State. The Secretary of State can then intervene if he or she decides that the person is being prevented from making a personal copy, the right to which is provided by this regulation.
This has little bearing on listening to music; most obvious forms of personal copying are achievable. However, one of the areas where I suspect this has interesting implications relates to video cassettes. Commercial video cassettes have copy protection schemes, and VHS/DVD combination recorders won't bypass them, meaning that people have not been able to transfer the content of commercial VHS video cassettes to DVDs. The implication of these regulations seems to be that this is likely to face a legal challenge, and copyright holders of copy protected videos could, in theory, be forced by the government to provide a means whereby owners can obtain personal copies without restriction.