I changed my name 'back' to my birth name cos I wasn't prepared to bring my child into this world with my abuser's surname. As it happens, I did it by deed poll. I think it cost me around £70, back in 2008. A deed poll is not necessary though (and I'm pretty sure the law has not changed). At the end of the day, whether you go by deed poll or simply start to use another name, by far the most important thing is that you do not go on to use either of the names for fraudulent purposes. Eg once you have changed, you need to relinquish the name you have lost and never use it again, unless for example you bump into into someone you used to know and you have to say your old name so they know it's 'you'. I have to do this occasionally but I always mention it don't go by that name any more.
The worst thing you will have to do is tell your bank, building society, pensions, credit cards, GP, hospital, dentist, benefits (probably department by department!), etc., and every organisation who deals with your child/ren (gp, hospital, dentist, school, cahms, out of school activities - the list will seem endless. I have several (puny) pensions and one of them, well, I gave up. They still write to me in my old name and I always quote both names if I contact them while stressing I do not use the old one any more. Doing it without a deed poll is just as legally valid, I believe, as doing it with one.
Just one thought, I recently learned that when someone dies, there is some sorta one stop place where advising that one organisation means everyone the deceased person had dealings with will be notified of their demise. Maybe this can be done similarly, somewhere, for name changes? (Probably not, but wow that woulda been ace for me in '08!)
Good luck whatever you do. XxX