Long-suffering shareholders in Lloyds Banking Group could see some cheer from the government's plans to sell off its 39% stake.

This week UKFI, the body which holds the Government's stakes in Lloyds and RBS, said prospects for the sale of Lloyds were now much better, while warning that institutions rather than small investors would get the first opportunity.

The sale of RBS, however, was still facing questions over the business model, UKFI said.

According to some institutions, Lloyds shares are set to continue the recent momentum which has seen them double in the past year, and this week regain autumn 2010 levels testing 70p, as interest in the sell-off builds.

Star fund manager Richard Buxton has Lloyds shares worth £12.3 million, the biggest holding in the £279m UK Alpha fund at Old Mutual. He believes that if the Government does move to offload the first 10% of its stake, the issue would be "hugely oversubscribed" and says that when the sale comes "if there is a modest discount to the share price, it may be an attractive opportunity to top up".

Lloyds shares were sitting at 161p five years ago this weekend. They had halved by mid-November and sunk to 28p by February 2009, briefly topping 75p in September 2010 before slumping below 25p in late 2011. The past 12 months, however, have seen a steady rise from below 30p in late July last year.

Mr Buxton expects the shares to rally substantially as new investors are attracted to the sell-off, claiming he can see considerable further upside.

Another fan is Steve Davies who runs Jupiter Undervalued Assets and Jupiter UK Growth, where Lloyds is again the biggest holding at 7% or a combined £70m of shares. He too sees upside ahead because the current share price does not value the bank's improved future earnings which he puts at 8p to 10p.

Over at still beleaguered RBS, shareholders will recall painfully that the five-year peak was in early September 2008 when the shares were just below 240p (2400p in today's price).

At the end of 2011 they dropped below 20p (200p), the high water mark in the past four years has been 558p, and over the past year they are up more than 50% to this week's levels above 325p.

Unlike RBS, many Lloyds shareholders still hold their shares as 'windfall' payouts from the former Halifax building society when it demutualised in 1997. The average 350 free shares were worth £2555 at that time, but after the merger with Bank of Scotland in 2001 the shares motored ahead, peaking at 1167p in February 2007 and taking the average windfall value to £4,084. However, by October 2007, with the price already back to 911p, the bank said 2.2m shareholders out of the original 7.6m still held their shares. The same number of Lloyds shares today are worth under £250.

UKFI suggested that following Lloyds' half-year results on August 1, the Government may sell a tranche of shares to sovereign wealth funds at a premium to the current price, then in early 2014 place another big tranche with institutional shareholders.

With the sell-off of Royal Mail now looming, Charlotte Black at stockbrokers Brewin Dolphin notes the traps in some of the Government sell-offs of the 1980s for those who have similarly held onto their shares. "A buy and hold strategy for the duration would not have worked on all stocks, with the relative return from BT the most disappointing."

An investment of £100 in BT when it was floated in 1984 attracting 2m small investors would have been worth £113 at the end of 2011, although the shares did rise to over £10 during the dot-com boom, and dividends are excluded. Similarly British Airways did not produce the hoped-for golden returns.

But an investment of £100 in the 'tell Sid' British Gas on flotation in 1986 would now be worth £1246, an increase of 1146% excluding dividends.

"Investments in Severn Trent, Powergen and National Power would all have outperformed the market," says Ms Black. She adds: "But Royal Mail will not be a dead cert and indeed we couldn't even hazard a guess at its merits until we know the terms of the offer."

The signs are that only a small slice of the Royal Mail sell-off may be offered to private investors, much of it being bartered with 'bookrunners' for institutions.

A recent report by the Association of Private Client Managers and Stockbrokers and brokers Peel Hunt called for the Government to engage more directly with 'Sid', and guarantee tranches of Lloyds, RBS and Royal Mail to ordinary investors.

Steven Fine, managing director of Peel Hunt, commented: "Current listing rules all too easily allow bookrunners to bar retail investors from the float. This means that the man in the street is prohibited from sharing in the success of UK companies, whilst hedge funds and asset managers reap more than their fair share of rewards."