I am an engineer (Electronics B.Sc. and Aerospace Systems M.Sc.)
Yes, depending on the chosen specialism, you must be prepared to go where the jobs are. Civil Engineering is all about large infrastructure construction projects. An engineer cannot do the job without going to the places where the construction is taking place.
Since all of the best engineering companies are global players, then a solid career path will inavariably require travel and quite often staying away from home - sometimes for protracted periods.
Whilst that is true for big multi-national consortium projects, there are plenty of other engeering jobs which are home based. Electrical and Electronics, Mechanical, Aerospace, Marine, Computer Systems, Chemical, etc. All have offices spread throughout the country and chances are that there will be something commutable.
Engineering degrees are also sought after by employers in many other unrelated industries: finance, commerce, marketing, production, sales, project management, IT, patent law, telecomm's to name a few.
It's because engineering degrees are some of the hardest and most rigorous alongside medicine, law, physics etc. The skills acquired are very transferable: science, numeracy, literacy (yes you have to present and publish your work concisely and without error), verbal communication, project management, professional relationship building, personnel management, creativity, complex practical problem solving, business management, health and safety, legislation etc. etc.
All are the skills needed to execute a professional engineering role.
Be warned: Engineering is not for the faint hearted. Mathematics pervades everything. Some engineering degrees have far more math's content than others. For instance, electronic engineering uses every math's topic covered in FP4 extensively and way more besides in far greater detail and you will be delving into it from day 1 of an engineering course. It doesn't ever let up. So you better love math's or your life will be a misery.
In short, Civil Engineering is one of those careers that requires the professional to follow the work be that in the UK or abroad. To get in with a chance of the big players, you will need a very solid degree (at least 2:1) from a good engineering university. (Imperial, Cambridge, Bristol, Manchester, Bath, Southampton, York etc.)
Do look at other engineering degrees besides civil, they may give you a better compromise for your particular personal circumstances. And do be cogniscent that engineering degrees are highly valued.