There are various ways in which a photograph or other artwork may 'derive' from another. The most common example is montage, where elements of multiple images are combined to make a new but 'derivative' work.

Compositing in this sort of manner is very routinely done by photographers and graphic designers. The new work will be copyright of its author, but infringement will arise if permission was not obtained for inclusion of someone else's copyright imagery. The owner of the original can then sue for damages or even claim joint copyright in the new work.

Note that you do not have to use an entire work for this to arise, even small elements cut from the whole are problematic. Nor does modifying those elements avoid problems unless they have been altered to the poiint that they are unrecognisable. If recognition is possible, it's an infringement.

Plagiarism, where a new work is based wholly or in part on someone else's copyright work, may also be a form of derivative work. Again, recognition of the original is the key factor.

There are not at present any special fair use provisions for derivative works in UK law, although legislation to permit fair use for the purpose of parody is expected, having been recommended by the 2007 Gowers Report