Royal Mail shares could hit double the government's original offer price, according to a leading City analyst, as the government faces criticism for undervaluing the 500-year-old communications firm and costing taxpayers hundreds of millions of pounds from the sell-off.

The government sold Royal Mail shares at an offer price of 330p ahead of the delivery business's flotation onto the London Stock Exchange, but demand was so high that the shares surged after their debut on the market. Many would-be investors missed out in the initial over-subscribed share offering.

"I don't think it's ridiculous at all for us to hit 660p on that, because it's only another 10% to 15% from where we are now, even though it has weakened a bit today, it did still very briefly at 8am set an all-time high again," said David Jones, chief market strategist at IG, to IBTimes UK.

"There still does appear to be a lot of momentum and enthusiasm behind them still, I think."

As it stands at the time of publishing, Royal Mail shares are around 80% above the offer price. Jones said there was not the level of selling in the early days that had been expected, which has supported the share price.

"Clearly, lots of people, whether institutional or private investors, didn't get the allocation that they wanted in the initial float, so that's kept interest reasonably healthy," Jones added.

There has also been some suggestion that Royal Mail could eventually be the subject of a takeover, which Jones said is "not doing any harm either".

"You probably have to say, on fundamentals, on what we know at the moment, to compare it to something like Deutsche Post - a natural competitor from Germany - Royal Mail is starting to look maybe a little too expensive, but saying that there' s still the appetite there to be a buyer," he said, adding that there should be no severe correction.

"I wouldn't be expecting any major correction or any major sell-off. I think the people who have been buying for the last couple of weeks are probably in it for the long haul. They're not looking for a quick turn," he said.

However, Josh Raymond, chief market strategist at City Index, told IBTimes UK that "whilst our clients have been net long Royal Mail shares ever since its market debut, we have progressively seen over the past week traders lock in some of their gains in case a market correction starts to take place."

"There were original expectations that shares could hit as high as 500p a share and so the rise to 595p remains surprising and aggressive," Raymond said.

"The option to buy into a historic British institution such as the Royal Mail attracted a broader base of investors, some of which have emotional ties to the company and will likely sit on their shares for a long period of time.

"This was a once in a decade IPO. The euphoria surrounding the IPO is however starting to calm down now and this is where share prices start to reflect a more fundamentally realistic valuation and so we need to analyse share price demand over the next month or so."

Vince Cable, the government's business secretary, defended the 330p offer price in a letter to MPs.

"Delivering value for money is about more than just the level of proceeds received on day one," wrote Cable to parliament's business select committee.

"Our long-term strategy to safeguard the universal service and deliver value for money for the taxpayer involves not only getting good value for the initial stake sold but also getting good value for the residual stake held by government (30% of the Company assuming exercising in full the Over-allotment Option), and leaving Royal Mail in a strong, sustainable position capable of accessing the capital markets in the future."