If the alleys are public rights of way, then, as Toureman states, the council may use a Footpaths Order to close them. They can't make such an order, however, unless the Secretary of State has already designated the location as a 'high crime area'. Otherwise it's almost impossible to close a public footpath.
If the alleys are not public rights of way, the council may be able to close them without a Footpaths Order. It's likely, however, that local residents will have covenants in their house deeds entitling them to have rear access to their properties. As such covenants can't easily be removed - it usually involves a special Act of Parliament! - the alleys would have to be closed in such a way as to ensure that each householder can still get to the rear of their property (e.g. by suplying keys to locked gates). There would be no obligation upon the council to fund these access changes (i.e. they might insist that the householders pay).
Either way, your first course of action should be to speak to the relevant person at the local council. (Job titles vary. It might be the 'Rights of Way Officer' or 'Footpaths Officer', for example). He/she will be able to tell you whether the alleys appear on the 'definitive map' (i.e. whether they're public rights of way) and be able to provide further guidance.
Chris