Who owns the wall between two properties

I am a director of a freehold management company for a small block of flats. We have a boundary wall with a footway leading to a large estate of 100s of flats. There are some problems with this boundary and it is not clear on our lease who owns it. If I order the title deeds for one of the many flats on the estate, is it likely to indicate the ownership of the wall? We are thinking of engaging a solicitor to escalate the issue, but I do not want to spend money on the solicitor doing a search that I can perfectly well do myself. Grateful for any advice.

Emily - in my experience it's unlikely that the registered information will be definitive. However even if it's 'silent' re such matters that can still be important in any discussions to be had with neighbours re who is responsible for what 
Have a read of our blog article for guidance - Drawing the line on boundaries – HM Land Registry