Certain cemeteries are with the agreement of burial rights owners [BRO] are using such spaces and normally the headstone is reversed and the new inscription would be shown on the new side [now the front]. The Ministry of Justice which has charge of Coroners and cemetery policy operates a committee [Burial and Crematoriums Advisory Group]. There are various representatives on the Group including the National Federation of Cemetery Friends. The aim was to bring forward a draft Legislative Reform Order (LRO) which could amend the Burial Act 1857 and other primary legislation in order to reform the processes governing the exhumation of human remains, the redevelopment of burial grounds and the closure of churchyards, together with some minor reforms to other areas of burial law. Core burial law dates back to 1857 and in 1977 some nearly 40 years ago new regulations were introduced under the Local Authorities [Cemeteries] Order. This permitted graves purchased a 100 years earlier and not used to be recycled by the LA. The example that you quote clearly raises other issues for example where the original BRO is deceased or family cannot be traced, should the ever increasing pressure on burial space now justify adding new burials. There are also religious consideration to be taken into account. Sikhs use only crematoriums but an increasing Muslim population which requires burials reversed the trend in this country especially since the end of WWII to go for cremations instead of burials. Some boroughs have literally run out of burial space and pay [often at an enhanced rate] to use burial grounds in other boroughs so it becomes a pressing question which the national government will need to address. Burial Rights Owners are approached by the local authority to renew the use of the right of burial after say the 50 or 100 year term which is normally for another 25 year term but in Cornwall the grant is for 10 years again indicating the pressure on burial space.
With the change of government to the present Conservative/Liberal Democrats coalition the new incoming ministers have now reviewed the position. They conclude that with the government's existing commitments and priorities for legislative reform in other areas, there seems little opportunity to modernise burial law in the short to medium term. Ministers have not yet reached a decision on the associated question of whether to take forward proposals to reuse old graves, but the matter remains under consideration. The citizens of this country will hopefully by bringing the topic into the open for discussion alert their MP's that the subject will not go away and perhaps it deserves a higher priority in parliamentary time.
A number of individual local authorities have reported an interest and some London cemeteries are able to reuse under local legislation. City of London Cemetery has started to re use such graves.
Common graves of course remain the property of the council and it has always been the policy to continue to add burials over a period of years until the grave is full.