More space could be made available for new burials by exhuming any remains after a set period and re-interring them deeper in the same grave.
The "lift and deepen" system of re-use was recommended in a report by the Environment, Transport and Regional Affairs Committee.
The report called on ministers to introduce laws permitting burial in re-used graves as soon as possible.
Andrew Bennett, chairman of the committee said: "We were taken aback by the sheer magnitude of the problems facing our cemeteries.
"The problem of underfunding has been exacerbated by poorly-trained staff, confused legislative responsibility, and neglect by both central and local government.
"The result is unsafe, littered, vandalised, and unkempt cemeteries which shame all society in their lack of respect for the dead and the bereaved."
Low priority
Mr Bennett said the "almost complete failure" of public authorities to address the problems faced by cemeteries was inexcusable.
The report criticised ministers' "hands-off approach" for giving local authorities "carte blanche to treat cemeteries as the lowest of low priorities". The committee added that the government must not "abdicate responsibility" any longer.
Local Government Minister Hilary Armstrong was criticised for not taking the problems faced by Britain's cemeteries seriously enough as part of the government's vision of an urban renaissance.
The report concluded: "If the public are to continue to have access to affordable, accessible burial in cemeteries fit for the needs of the bereaved, there appears to be no alternative to grave re-use.
"We ourselves are of the opinion that legislation should be introduced allowing burial to take place in re-used graves."
Among other recommendations, the committee advised local residents worried about the state of their graveyards to apply for National Lottery funding, and called for a "standing inspectorate" to be set up.