Well, if you're looking to go into the arts or become a doctor, engineering is probably not very useful. If you plan to go into engineering, finance, economics, business or STEM in general, then it can be useful.
Engineering is a very broad word though. There are a good dozen or so fields such as the mechanically related (mechanical, aerospace, automotive, etc), civil, chemical, nuclear, etc. There is some crossover between the like minded fields, but you should try to choose a subject which best represents your goals in the future. I believe Oxbridge tend to do "general" engineering degrees where you specialise in the final year, but plenty of places will offer the "pure" degree in one subject area.
So it really depends on your goals. The maths elements and analytical skills are transferable to many other fields after graduating. It is quite broad in terms of the scope of employment. That said, people who did maths or physics should be able to get into engineering too. However, there is quite a lot of specialism at degree level - Someone studying maths would have no clue about material properties, using tools/CAD or generally the ins and outs of engineering, but they would have the mathematical capability to go into that area.