Could someone describe for me the differences between top down normalisation and bottom up normalisation with regards to databases, namely relational databases.
I expect you mean top-down design vs bottom-up design - normalization being just one aspect of the methods and principles you would use to complete a database design.
Top-down means you start with a set of requirements. Usually you begin by identifying the types of things that you need to represent data about and then identify the attributes of those things, which will become attributes in tables.
Bottom-up design means you are given some kind of data structures to start with, e.g. a list of attributes or tables and attributes which you need to incorporate into a design. Typically this might happen where you have an existing database or data source, as is common in business intelligence or data integration projects.