That unusual combination meant he was a natural choice to replace Lord Marshall as chairman of Municipal Mutual Insurance after his predecessor died in 1990.
MMI needed someone who could understand the requirements of its local authority customers and handle financial pressures on the group.
Mr Stonefrost, then 63, was already a non-executive director of the company.
His move took pension fund managers by surprise. Why was he moving from British Rail's pension fund, where he had built up a reputation as a thoughtful and original manager?
Cynics suggested he was moving out of the public sector to make money before retirement. But friends and former colleagues dismissed these suggestions.
One said: 'He went out of a sense of duty, not of advancement. That would not be Maurice at all.' Another said Mr Stonefrost was a public servant at heart. He would see a problem and, if he was at all involved, would feel it his duty to sort it out.
His involvement in local authorities is long standing. Having started at Bristol council in 1951 he went on to work for Slough, Coventry, West Sussex and the Greater London Council, where he was director general before it was wound up.
This background in local government set Mr Stonefrost apart from other fund managers, most of whom have worked in stockbroking, money management or other parts of the City for their entire careers.
It allowed him to rethink the entire investment strategy of British Rail's pounds 7bn pension fund, where he was chief executive.
Out went many of the works of art for which the fund had become famous but had only ever accounted for a tiny proportion of its total value.
The art had been bought in the Seventies, when inflation was rising fast, as a hedge against increasing prices. In the event, the ancient Chinese horses, the Italian drawings and the French impressionists did keep their values, but not as well as shares.
As the works of art were sold Mr Stonefrost introduced a more conventional range of investments including shares, gilts and property.
Though he started by questioning whether these investments were right for British Rail's pensioners he ended by adopting a fairly conventional structure. The main change was a cut in property holdings from 20 to 10 per cent of the total.