The price hit £5.08 during yesterday's trading on the London Stock Exchange as Business Secretary Vince Cable admitted he was told before the float that the price could soar.
The new high was reached as he said bankers at Goldman Sachs, UBS and Lazards handling the sale persuaded ministers not to increase the offer price above 330p, fearing it could hit demand.
He said that, earlier in the preparation for the sell-off, the threat of strikes by Royal Mail workers left some potential investors saying they were not willing to buy.
An initial price range of 260p to 330p was set, with the lower end factoring in possible escalating industrial relations problems that might push it down.
Communication Workers' Union general secretary Billy Hayes said: "For Vince Cable to blame the low price on a possible threat of industrial action is laughable."
But Save Our Royal Mail campaign director Mario Dunn said: Mr Cable is directly responsible for the taxpayer losing hundreds of millions of pounds. He should do the decent thing and resign."