Having galvanised the heritage quango with his aggressive management style, the former newspaper executive had hoped to see his vision of a 4,000-acre Stonehenge Millennium Park on the Wiltshire Downs through to fruition.
But Sir Jocelyn, 64, is engaged in game of brinkmanship with his direct superior, Virginia Bottomley, Secretary of State for National Heritage, and the Treasury. Yesterday, after launching a churches restoration fund, he made plain he would quit if there is a further cut in EH's pounds 104m grant.
Sir Jocelyn's five year term ends next March and any successor for the pounds 43,000 post would normally need to be in place as an under-study for six months.
Mrs Bottomley is understood to have asked Sir Jocelyn to stay on but the former managing director of Express Newspapers is keeping her waiting. He underlined his concerns over funding at a breakfast with Mrs Bottomley last week in Bournemouth during the Conservative Party conference.
EH's grant is already due to be cut by pounds 44m in real terms over the next four years and it has been told to expect worse. Sir Jocelyn has warned the Government in private that the agency may have to stop giving grants to local authorities under Conservation Area Partnerships.
Last year, grants totalling pounds 8.5m were made under the scheme, preserving the architectural character of whole streets and blocks of buildings.
Sir Jocelyn said he would have to make up his mind "very soon" whether he wished to stay on. Asked what were the deciding factors, he replied: "It depends on the level of funding."
He had acknowledged, while launching the churches fund, that congregations who depended on EH for help with repairs had been concerned about Government imposed cuts.
Referred to by staff as "piranha teeth", Sir Jocelyn's style was the subject of comment last July when EH's chief executive, Chris Green, resigned over "alleged administrative irregularities in the discharge of his duties".
Sir Jocelyn has made Stonehenge the great cause of his chairmanship. His aim is to see the 4,000-acre World Heritage Site reunited, with roads removed and the public able once again "to touch the stones".