Lease shows access to back of shared property on wrong path

We are in the process of selling a flat in a block of 4 flats.  The rear access to our flat is shown on the lease (in dark grey) as a path which doesn't exist, to the left of the block of garages.  There is a path. to the right of the garages, which exists and is correctly reflected on the leases of the other 3 flats in the block.  We can only assume that in 1979 when the block was built, only one path was created.  The issue of it being incorrectly shown on the lease for our flat hasn't been noticed before despite the flat being sold at least 2 times.

However, our buyer has noticed and it is suggested a Deed of Variation will be required.

Is this really necessary to correctly reflect the access path ? If so, is this an 'easy', straightforward variation to register ? 
and how quickly can a Deed of Variation be registered, so that we can get the sale completed ?

Also, the garages themselves are built in a line, so it is actually a rectangular shape, rather than each one being shown as slightly set back in the lease - is this also something we would need to correct ?

Thank you in advance...  

Andrew - if the lease is 'missing' a key right then I suspect a deed of variation is the best way forward to resolve it. Likewise if something else is awry and needs amending/correcting in some way with the landlord.
A deed of variation that varies the rights would wait 4-5 months. One that varies the actual extent (demise) would wait 14+ months currently.
But those timescales are not relevant here if you are trying to sell and have a confirmed buyer. You would need to submit an application to register the DofV and then request expedition to keep the wait time as short as possible
Do speak to your conveyancer re the best way to achieve things