''We hail Britannia, the grand old lady of the sea!'' In a speech brimming with patriotic fervour, Edinburgh's Lord Provost, Eric Milligan, welcomed the royal yacht Britannia into Leith Docks yesterday morning.

In understandably ebullient mood, the provost declared himself to be ''cock-a-hoop'' alongside the people of Edinburgh at the arrival of the decommissioned yacht.

After months of speculation, bitter civic rivalry and the blasphemous suggestion from the original naval architect to sink the yacht, ''the best of British style and prestige'' was finally towed into the docks just after 8.30am. Taking a two-hour breather just outside the port after her 560-mile tug trip from Portsmouth, Britannia cast a regal gaze towards her ''commoner'' subjects of the future.

Pockets of grinning civic leaders paced the quay, the Forth Port Authorities officials appeared suitably smug at having won the hotly contested competition. The media swarmed about, staging photographs.

But it was an eerily quiet crowd who watched Britannia. Even for those landlubbing Edinburghers, the sight of a once majestic yacht being towed in like a decrepit monument elicited a poignant response.

Alice McGregor, 83, whose husband, Archie, worked on the yacht, was in agreement with the ship's designer, John Brown, 96. ''It's not right, it having its innards torn out and brasses all gone to be made into some kind of floating attraction,'' she railed. ''It should have been sunk as a mark of respect.''

The civic fathers and mothers were too busy puffing up with pride to listen to criticisms. As the newly painted blue, red, and gold trimmed ship was manoeuvred into place the pipe band of Lothian and Borders Police struck up, the five fresh-faced sea-cadets shuffled into professional line and the inadvertently comical High Constabulary in penguin suits raised their top hats in salute.

From the yacht deck we half expected a gloved royal wave. Instead, the men in the day-glo jackets and orange hard hats arranged the naval ropes round the podium of dignitaries.

The plaudits rained heavy. Leith was a ''smashing'' place, declared Donald Dewar, Britannia was ''fantastic'' and ''wonderful,'' cried the Forth Ports Authority spokesman. Only when Eric Milligan acknowledged the justice of a Scottish-built ship returning to Scotland did the crowd break into enthusiastic applause. Perhaps, it had been infiltrated with disgruntled West Coasters?

Not at all, said Margaret Wood. She summed up the retrospectively benevolent attitude voiced by most Leithers towards their losing Clyde cousins.

Referring to John Brown's shipyard and Engine Works in Clydebank where the yacht was built in 1953, she admitted: ''I do think that Glasgow should have got Britannia. But I'm pleased that such a historically important vessel should come to Leith because it means that the tourists will start to venture down to Leith during the festival rather than avoid us, as they usually do.''

With perfect timing, Liesel and Peter Green from Minnesota chipped in that they are in no need of a convincing prod. Decked out in maritime T-shirts, Liesel enthused: ''We really feel that we're witnessing a special moment this morning.'' Though she has one gripe.

''I think the Queen should have been here to make it a proper occasion.''

However, one cynical wag was in doubt as to the fate of Britannia. ''Aye, they'll be smashing her up for commemorative keychains in 10 years' time!'' he predicted. Naturally out of Eric Milligan's ear-shot.