So, their notice is incapable of holding you liable for the charge as the registered keeper. They know this, as their notice states they'll be pursuing you on the 'assumption' that you were the driver. Because you have categorically stated you were not the driver, and even offered evidence to support this, any assumption you were the driver is clearly an unreasonable one, and if they have any sense they'll not try and take this to court.
Parking companies, however, rarely have sense, so they may well try. As b789 said above, keep your eye out for a Letter of Claim. If they issue one, come back here for support. If you move house before the matter is concluded (they have 6 years from the date of parking to make a claim), write to them to inform them of your new address. The last thing you want is for them to secure a default judgement by issuing a claim to an old address.