Could you get a job in engineering after doing a maths degree?

It really depends on what kind of engineering job you are looking for...there are jobs which might require specific knowledge of either CAD, CAE or other experience with specific modules or labs, which you won't be able to have with a maths degree. There are other jobs, which might be more mathematically demanding, where you might fit in, but you have to be more specific and check the requirements for every job and company you are interested in.

A relevant MSc is always a plus...

Thanks for the info I was thinking mechanical engineering or aerospace engineering

^^

At a fundamental level engineering is about applying principles to a particular problem to come up with a real-world solution, whereas maths tends to be a more esoteric, 'pure' subject (obviously there are exceptions to both of these). So you'd be competing for jobs against graduates who will have 'hands-on', practical experience gained through labs and probably work attachments. If you meet the minimum requirements then by all means apply, but be prepared to work hard to convince recruiters.

If you know you want to work in engineering why not apply for it in the first place?

I am guessing it all boils down to relevant experience.

Almost every single engineering job I have seen has specified an engineering qualification (HND/degree etc.) as a requirement. That's not to say that it's impossible but it's obviously much more difficult than if you have a relevant qualification.

Depends on the nuts and bolts of the job...

I would like to do maths behind the design but not necessarily do the designing if that makes any sense