Boundaries

I moved into my house last year and am having my garden sorted out as it is overgrown.  I told my next door neighbour and she asked if the gardener could trim a hedge that is between our properties so it’s a bit lower as is hard to trim because it’s so high.  I was looking at the deeds of the house.  It says in the original deeds from 1967 that it is my responsibility to maintain the boundary on the left hand side as you’re looking at the house from the road which Is that hedge.   On the original plan of the street it’s  labelled with an inward T.  However when I looked at the information that the seller gave me it said that I maintain the back and the right hand side.  Who is responsible for the boundary.

Alison - the simplest answer is generally whoever you/your neighbours agree is responsible.
The information the seller passes on is usually what they have done/understand to have been the agreement between them and their neighbours at the time. It's their understanding only and based on what each of them has done to date.
The 'T marks' you refer to tend to relate to old deeds/documents and covenants entered into at a moment in time, in this case 1967. The covenants often include what are known as restrictive and positive covenants imposed at the time for the benefit of other land/property as defined in the Deed itself.
Restrictive covenants are of the type that state what the property owner can't do for example keep chickens, sell alcohol etc and they bind the land continuously 
Positive covenants are the type that state what the property owner should do and invariably that is a single covenant re the boundary. They bind the purchaser at the time, in 1967, and may or may not then bind later buyers depending on whether each buyer agrees to stick to it, to put it very simply.
So you have a mix of information it seems and as such I would suggest asking the neighbour(s) what information and understanding they have and then reaching an agreement as to who does what etc. Shared information and understanding can often resolve matters but very much down to you both to decide.
Drawing the line on boundaries – HM Land Registry (blog.gov.uk)