Right, I'll fill in a few more details which might be useful, and a bit of an update.
1. I'm aware that persuing a trespassing claim would most likely be fruitless, but my point would be that if they won't do anything because of their "mistake" and expect me to pay a £50 fee because of "my" mistake, then this makes the contract inherently unfair as they can breach the contract without penalty whatsoever.
2. The LA entered the property to remedy an oversight, there was a wardrobe that was left behind, we requested that it be removed prior to our moving in, but this did not happen. We enquired when they would remove it, they offered to send someone round that day, if that was ok with us. We declined (in an email, so there is proof of this declination) on the basis we would prefer to be in, since we have a cat and worried that it would escape. We came home from work to find the wardrobe gone, and received an apology from the LA that she hadn't seen our email until after dispatching someone to collect it.
3. I had already enquired when the bank received the mandate, it was received on 13th of september, 2 days before rent was due, and therefore, the SO was set up ON the 15th, and thus too late to make payment. I have brought this to LA's attention, and she states that it was sent out 1 week after signing tenancy agreement. She claims that since the contract states that "The tenant agrees to pay the rent on the days and in the manner specified to the LA" that it is my responsiblity to ensure this payment is made (I can see that makes sense, but does this extend to ensuring the LA is performing their job properly)
4. The LA have not offered proof that the SO mandate was sent as promised, and actively tried to suggest they didn't need to supply it.
5. Unfortunately I cannot remember whether we were compelled to fill in the SO mandate, or whether we could of set it up ourselves. The latter option was certainly not offered to us (if this wasn't offered then surely it was not up to us to ensure the mandate was set up correctly? I doubt I'd make that stick, but it does annoy me that it was made to appear that we couldn't sign the tenancy without it, but somehow it was our duty to ensure it was set up!)
6. Regarding the £50 being a penalty, it is specifically described as an administration fee in the contract if the rent is overdue.
Right, I think I've addressed all the points raised in the posts above. Now for an update. When we were informed of this "adminstration fee" we were told that if it was not paid, it would sit in our account until paid i.e. be that next month or at the end of the tenancy (these are almost the exact words that the LA used). We have today received an email informing us that we haven't paid (duh!!) and that if it is not paid by the next due date, they will deduct this fee from our next payment. Which will according to them mean that we will be late on our rent, and potentially incur another £50 fee as well as now oweing £50 in rent arrears. Obviously this will continue until it is paid, so on a 6 month tenancy we will incur £50 in fees and £250 in rent arrears. We may pay the fee, but ensure any invoice is marked with paid under protest. What do you think?