If you recently purchased then ask the solicitor who did the conveyancing for you as they should have looked into this - it would appear to have been raised by the existence of the statutory declaration.
By the sounds of things, the alleyway is within their title (though this should be checked) and that the previous occupiers of your property have used the alleyway hence the statutory declaration.
It's nice that they take your wheelie bin out but is that another way of them stopping you from accessing directly?
A statutory declaration is a mere statement of use, it does not form a right and, in essence, may only prove the existence of use over a period of time which may provide evidence in a application to accrue a right.
It may be backed by indemnity insurance for lack of formal easement (right of way) but that will only, depending on the terms and conditions of the policy, provide an insurance fund to compensate for the loss of the access (how do you quantify not being able to take your wheelie bin out more directly once a week!) or maybe to fund certain action in trying to obtain a formal right.
That said, if access has been had since before 1973 then there is a fair chance of obtaining a prescriptive easement. Do you know if your solicitor attempted to have anything about the alleyway registered at the Land Registry?
The previous type of use (what it has been used as access for) should be considered so be careful about relinquishing too many rights which could be deemed reaoosnable).
This is the Land Registry's practice guide..
http://www1.landregistry.gov.uk/assets/library /documents/lrpg052.pdf
Many of these kind of cases need to be put in context. Would you really want to end up in a neighbour dispute and potentia