Garden Wall ownership

The garden wall bordering my neighbour's property has collapsed (into our garden) and we are in dispute over whose responsibility it is to fix it. She claims that as the wall is on the left hand side (looking from the road), it is our responsibility to fix. As 'proof' she has provided the TA6 form the previous owner filled in when the property was sold, stating that this is the case. I have the title plan and register for my property and it does not show any boundary responsibilities. My understanding is that this suggests the boundary wall is shared. Some basic googling suggests the 'left hand rule' is an urban myth. Any advice on the legal situation here would be much appreciated.

Tim - it's legal advice you need if you want to understand the law re such matters. Our online blog explains the general points re boundary ownership/responsibility from a registration perspective - Drawing the line on boundaries – HM Land Registry 
A TA6 is completed by a seller and is essentially what the seller believes/understands prior to selling. Your seller may have also completed a TA6 and stated the 'opposite'. The TA6 is like everything else generally re boundaries, simply information to share/include in the discussion