Charged £36 for switching to a different supplier ...

Question

I signed a 12 month phone and broadband contract last September with BT, and received a renewal notice a month prior to my contract being up to say that I should let them know if I didn't want to renew, otherwise my renewal would go ahead on 19th September.  
This year I decided to try a different supplier, so I signed up with this other company at the start of September and they contacted BT to say that I would be switching - this notice was given two weeks before 19th September.  My switchover date was 26th September, so I had one week further with BT beyond my 12 month contact, which BT didn't state would be a problem.  BT sent a letter confirming my account was being terminated, and stating that I would be charged £0.77 for switching.  It seemed a bit strange to me that I would be charged for switching suppliers, after all it doesn't cost BT anything apart from losing my custom and I wouldn't have thought it was in line with competition laws to try and put charges in place to discourage people from switching, but I thought nothing of it as it was such a small amount.
However, I've since received an email from them saying:
As you're stopping your service within the minimum term, you'll need to pay £36.170002 for stopping early. This fee is usually based on the number of months left on your contract.
But I'm NOT stopping within the minimum term, my minimum term was 12 months which I completed - and I never signed a new contract with them, and I told them with plenty of notice that I would be switching elsewhere, so there are NO months left on my contract.
I can understand that I will be charged for an extra week of service, which by my calculations for unlimited evening and weekend calls (£3 per month plus £10 line rental) and 40GB monthly broadband (£18 per month) totalling £31 per month, for 7 days that works out at about £7, which is what I would expect my final bill to come to.
Anyone else had this issue?  It's odd that I've received two different letters via different communication channels (one in the post and one via email) which say contradictory things about termination charges.
Advice and help would be much appreciated.  Previously I had a reasonably good image of BT and would have considered switching back to them next year, however that prospect becomes less likely the more they mess me around with this.
Thanks for any help you can give,
Tdot

Answer 1

Thanks for responding, in answer to your questions:
1. No I didn't get a MAC code from them, I didn't realise I even had one, they didn't mention this when they contacted me and said it would cost 77p to switch.  As they didn't mention it in their letter when they had the opportunity to tell me about any additional charges, I'd be very annoyed if they charged me when there was another way of doing it which would exempt me from those charges!
2. My new supplier contacted BT straight away and BT sent a letter to me confirming that my contract would be ending. As a result, I didn't think I'd need to contact them to say it would be ending - surely they already knew if they contacted me to let me know when my service would be stopping?
I did email them and they have got back to me saying something about a fault with my bill, and that everything should be fine once my final bill is issued.  I will wait and see on the final bill what happens, then if it's not to my satisfaction I'll put in an official complaint.
From a look around this forum, the MAC code issue seems a common one.  Any ideas how it usually pans out?  It seems to be an ongoing issue on quite a few posts.  Is there anything I can do now the switch has occured?  I assume not, but it's worth a try.
Many thanks,
tdot