Shares in Royal Mail have closed a third higher following their first day of trading on the London stock market.

The 34% rise from the 330p offer price has fuelled the debate about whether they had been priced too low in order to guarantee a successful privatisation.

At one stage the increase inflated the value of the near 500-year-old company to £4.5 billion sterling in one of Britain's biggest state sell-offs for decades.

It came after criticism from the opposition Labour party that the government was short-changing taxpayers.

The stock hit an early high of 456 pence after the hugely oversubscribed sale of a majority stake had been priced at 330 pence per share, generating £1.7 billion for the UK government before fees and a possible "overallotment" option of extra shares which can be sold depending on demand.

By around lunchtime, the shares were trading at 440 pence.

British Business Secretary Vince Cable again denied the government had undervalued Royal Mail. "You get an enormous amount of froth and speculation in the aftermath of a big initial public offering of this kind, it's of absolutely no significance whatsoever," he told the BBC.

"What matters is where the price eventually settles and if we look back on this in three months, six months time, or indeed years to come, that's what we're really interested in," he added.

After receiving around £27 billion worth of orders for the £1.7 billion worth of shares on offer, the government allocated 33% of the offering to members of the public, with the rest going to institutional investors.

The appeal of the stock had been boosted by a lucrative dividend promise for shareholders. Royal Mail is to pay a final 2014 dividend totalling £133m, equating to a full-year payout of £200m had it been listed for a full year and giving the shares a full-year implied yield of 6.1%. This is attractive at a time when a regular UK savings account is yielding less than 3%.

Cable said the bulk of shares had gone to long-term investors, mainly British pension funds and insurance companies.

Members of the Communication Workers Union (CWU), which represents postal workers and is holding a strike ballot over pay and job security, held a protest outside the London Stock Exchange on Friday in opposition to the sale.

The government handed 10% of Royal Mail's shares to staff in the largest share giveaway of any major British privatisation, with just 368 of the 150,000 eligible UK-based workers declining to take up their free shares. Staff are required to hold the shares for three years.

Royal Mail's public offering leaves the government with a 38% stake, but this could fall to 30% should it choose to exercise the overallotment option.

The shares, which could be eligible to join the FTSE 100 index of leading British shares at its next review in December, are trading conditionally until October 15, meaning in theory if the sale was cancelled the trades would be void.