On the first day of the shares in the newly privatised business trading on the grey market, before they officially go live on Tuesday, some Hargreaves clients have been unable to log in to their accounts as the website saw a surge in traffic.

In a series of tweets, the discount broker said the Royal Mail share offer had created “unprecedented interest” and it is “working hard to solve the problem”.

“All available staff are working on dealing lines and website, we are trading by phone but delays getting through, our sincere apologies,” a second tweet read.

Later the group posted: “We are sincerely sorry for anyone who hasn’t been able to trade this morning and are doing all we can to meet client demand.”

The price of Royal Mail shares soared well above the government’s offer price after conditional trading in the company began this morning.

In a move which exceeded expectations, shares in Royal Mail jumped 36% from the government’s offer price of 330p to 450p just after 8am when they began trading in the grey market.

Demand for shares has far outstripped supply, with almost 700,000 private investors applying.

In total the retail share offer was seven times oversubscribed, prompting criticism that the privatisation undervalues Royal Mail.

Private investors who applied for the minimum £750 up to £10,000 will receive shares worth £749.10. Applications for more than £10,000 will receive nothing.

Royal Mail shares will not be listed on the Stock Exchange officially until next Tuesday, with two days of conditional trading first.