If you want a job at the end, no offense, but you'll find it easier with an engineering degree than a natural science degree.
Engineering is ALL about applied mathematics, using it to deal with real-world issues. Physics is also, but with more abstract concepts, which are earlier-research and hence less applicable to the world we live in near-term. Mathematics is even further into abstraction. They all share the common language of mathematics. One is the exploration of that language, one is the study of the consequences of the language, and engineering is about using that language to solve problems, keep the world going around, and making money.
Electronics at A-Level is absolutely nothing like electronics at university. I studied the latter. Complex differential equations, Transforms such as Fourier, Laplace, numerical methods - all everyday tools to the electronic engineer. Yes, you might have to understand what a gate is, but when you're learning how mathematics makes them possible to be fabricated at component sizes of 14nm, then its orders of magnitude more interesting than using batteries and lightbulbs in a school lab.
With regard to slumpy - There are just as many engineers as mathematicians working on codebreaking, more engineers model fluid dynamics, do rocket science and again, probably just as many engineers work in finance as mathematical quants. Source - my peers who graduated with me.
It's highly transferable, engineering, and you can go into almost anything with it. Smack has already said that you can do engineering with minimal exposure to maths if you wish. The opposite is also true - there is always maths to be done, though generally using computers.
With regards to hands-on in engineering at university - most students are dissapointed with the lack of it- there are a few labs, but not many. If you like applied maths, then engineering will definitely suit you. Most engineering problems to be solved cannot be solved prototyping something in a lab, they involve hefty computer simulations, analysis of algorithms and a detailed understanding of the mathematics underpinning the problem.
Best of luck,
Stu Haynes MEng