Can't see the signs on street view - but at a guess paying via the website is not available at the Premier Inn - unless you have pics that show otherwise? You did have a conversation with their oppo, but they may not a record of this. Appears you were a genuine (repeat) customer at PI - in which case expending efforts to get them to get the charges cancelled is the best plan. You will probably have to go higher than the desk at the hotel, or even the local manager.
After that, trying to negotiate a settlement with Horizon (but I wouldn't hold out much hope...)
If not, then it will progress to court claim eventually - which they are likely to pursue given there is >£1k on the table. Generally any claim that is defended is discontinued, but in this case, given the value, they may not. There will be an opportunity for mediation in the claim process where a smaller settlement could be agreed.
However - as a genuine customer, getting PI to cancel them would be best, but it may not be easy!
