English Heritage senior landscape adviser Jenifer White said: "If the value of metal continues to rise, it is logical that park gates and roofs could be targeted."
She was commenting on churches, which recently made headlines for a 20-fold increase in insurance claims for theft of metal. Parks may be next, she said, especially as budget cuts were leading to lower staffing levels.
"If parks aren't staffed or well-used it could pose a threat. The problem isn't just theft, but graffiti, vandalism and buildings being torched."
White praised the restoration of Stanley Park in Liverpool, which refurbished the Isla Gladstone Conservatory and turned it into a concert venue.
White said English Heritage wanted local authorities to sign up to the Alliance to Reduce Crime against Heritage, a voluntary national network.
The initiative was launched by English Heritage, the Crown Prosecution Service and the Association of Chief Police Officers. Membership of the group is free.