Not sure where I stand. Was told one cost to leave and invoiced another

[#1]

Hi All,
First I should say that I have been in contact with Plusnet and their debt team are looking into my problem. I would just like a third party opinion.
I rang up a few weeks ago to let them know I was looking to switch providers and asked how much it would cost me to leave.
I was quoted 88 pounds to get out of my contract early. I decided this was OK and made the switch. Plusnet then sent me a letter telling me that if I were to leave then I would be charged 77 pounds.
A couple of weeks ago the switch went through. Today I get an email saying that my final invoice will be the best part of 230 pounds. After phoning they could not explain why I was given the previous figures. I made it clear that my decision to leave was based on the figures they had given me (which they have a record of).
So now what? What if they come back and tell me that there is nothing they can do? I can't afford to pay 230 pounds and don't know why I should when they failed to tell me that in the first place.
Where do I stand legally? Does the fact they potentially made a mistake calculating the figure in the first instance when I was thinking of leaving mean anything?
Thanks

[#2]

Leave this with me for now, I'm going to send off a few emails and see why we're trying to charge so much after clearly stating a lower amount.
I understand there may have been some sort of system issue that caused a lower amount to be advised, however I don't see why that should be your problem.

[#3]

Thanks.

[#4]

My support ticket was updated and I have been told that I have to pay the full amount.
FORGET IT
You cannot quote me one figure over the phone and then via a letter and then drop me an invoice for three times the amount.
The fact that your systems messed up is not my problem.
My decision to leave was based on the value you quoted me!
I will fight this every step of the way. What a disgusting way to treat a customer since 2009.
The direct debit has been cancelled (which Andrew at PlusNet told me to do on Friday).
I was told you would be in touch with me today. I await for phone call and look forward to hear how you can justify charging me 230 to break free of my contract when you sent me a letter, an actual physical letter, with another value on.
I look forward to hearing from you.

[#5]

As per my previous message, leave this with me for now as I am dealing with this for you.
At no point did I say I'd be calling you today with an update and I am still waiting for a response on the email I sent.
Again, please leave this with me for now and I'll get back to you via the ticket on your account later today with an update.

[#6]

A guy called Andrew stated over the phone that I would be contacted today I believe with an update.
Instead someone updates the support ticket and states that I need to pay the full amount.
How am I to know that I should disregard the support ticket?
Apologies if I jumped the gun

[#7]

I've discussed this with my manager now and updated the ticket on your account.
I've also made sure there's a note for our billing team to arrange taking a payment of the lower, previously agreed amount, once the current payment has failed.

[#8]

Thanks for your help Harry! Glad you could sort it. Really appreciate that

[#9]

No problem, feel free to let me know if there are any further problems with it.