There are two ways you can approach this.
Either try to see someone senior in the Midwifery department, and talk through your experience in an informal way. You can do this either by contacting them directly (you should have some phone numbers in your paper work), or by asking the PALS team to help you set it up. I'd do the latter, as they should be very supportive, and will know who you should best talk to. Hospitals I have worked in have been very keen on receiving feedback, and often the Chief Midwife is the person available.
Or you can make a formal complaint. You don't actually have to do this in writing, but it is usually better to do so, as you can be clear in your mind what specifically you are unhappy about, and what you would like the hospital to do about it. You may find it useful to ring up the hospital's complaint's department as they can talk you through the process, and will in any case manage the complaint as it comes in. You can write the actual complaint to the CE, the Chief Midwife, the Complaints Manager, or any other named person, but I think it is worth sending a copy to the complaints department, because they are charged with making sure complaints are managed within time frames etc.
Do not ask for compensation in the complaints letter, as this is handled differently, and if you say you have instructed a lawyer then the complaint will not be addressed as they will wait for the lawyer to contact them. If you still wish to sue after you have got a response to your complaint then you can still do so, so you haven't lost your opportunity. I don't think that it would be worth pursing legal action however, as from your OP it doesn't sound as if you have suffered any significant harm, so you would be unlikely to gain any damages. You can always ask your CAB or get a free consultation in the meantime though.
You do need to separate the two issues though, the first is about the fee for the room, which your husband or you can pursue, although since they have cancelled the bill I guess that has been resolved. The other issue is the standard of care, where you need to make the complaint (if you want to), or where you need to give your consent for your dh to make the complaint on your behalf.
The other thing you can ask for is a copy of your medical notes, either as a copy for you to look through, or (probably more useful) ask for someone from the midwifery team to go through them with you, so you can understand what happened.
As to whether any changes will be made, I think that is mostly down to the department, and how seriously the hospital takes complaints. I don't think that suing make more difference except when the sum is very high, or the incident high profile. For a hospital with maternity department I am afraid that legal claims are part of the routine, and only very significant claims are discussed at Board level. The Board will be concerned about the volume of claims, and seek to reduce them, and claims will be looked at in detail within departments, but then so will complaints.
Finally all NHS insurance is handled nationally, and all hospitals make a contribution to the scheme, so yes it does take away from the total pot for the NHS (and the money we all pay as taxpayers) so there is an impact. Just not directly on the hospital in question.
Oh and the Community Health Councils were abolished a few years ago now, in fact their replacement has also been abolished, and the new bodies not quite set up yet.
I hope all that makes sense! I used to manage a complaints department, so if you have any questions I am happy to answer them.