There are plenty of Christmas decorations on offer, but rather than straggly tinsel you have wooden eggs, hand painted with Estonian winter scenes, and glass baubles to decorate the tree.

There are also more unusual stalls, such as the one selling felt hats. I try on several and, being a fan of novelty hats, I’m almost tempted. Then I realise it might not get a lot of wear on the streets of London.

Huddled over a fire at one corner of the market is a blacksmith making his own wares, including candlesticks and ornamental iron pieces, as a crowd of shoppers gathers around him.

At the other end of the market are rows of food stores, serving up everything from hot chocolate to spicy sausages and apple strudel.

Situated in the middle of the Old Town, the markets bring the city alive during the cold and sometimes snowy months of December and January. There’s a romantic appeal to strolling through the narrow, winding streets, where shop fronts are filled with Christmas decorations, and sipping on cups of steaming, sweetly scented mulled wine.

After checking out all the stalls in the square and needing to walk off a hefty portion of strudel, I join a tour with local guide Denis Miromav, who points out the quirkier landmarks the untrained eye might miss.

There’s the ‘peeper statue’ of a bespectacled old man peering from a window overlooking the high street. Two legends surround the statue: he was either spying on his wife or watching young women doing laundry in a house across the road. Sounds like a bit of a perv either way.

Most of the historic buildings are located at the top of the upper town, thanks to it having been the former home of the bourgeoisie. Here you’ll find Toompea Castle, a complex including a pastel-coloured building which is now the seat of Estonia’s Parliament, and a fortress which has existed since the 9th century. From here there’s a great view across the city, with church spires and the Christmas tree from the Old Town market looming over the huddled roof tops.

» Erin Miller travelled to Estonia with Topdeck (0845-257 2515; Tours start from £649.

Dining with the president

For a night out on the town and a taste of hearty Baltic food, we head over to the Olde Hansa restaurant on a chilly evening.

The place is rammed, with big groups dining at the long wooden tables underneath dim, cosy lighting.

The waiters, dressed in pinafores that could have come straight from the set of The Sound Of Music, attend to our drink orders efficiently, serving up large ceramic jugs of pear cider.

But my attention is drawn to a heavy-set man in a suit standing behind our table and sporting an earpiece.

Sensing a bodyguard in the building, I begin to scan the room trying to identify if there is a celebrity within view. The tables near us seem to be full of families eating, though.

As I sit debating who the famous person is with my dining companions, there is suddenly a flurry of movement. The bodyguard is joined by another burly bloke and a man in a suit who, along with his two children, is quickly ushered out of the restaurant.

After watching the action unfold, we ask our waitress who the famous patron at the table next was. “That’s our president,” she replies with a beaming smile.

Well, if the food’s good enough for Estonia’s president Toomas Ilves, we figure it’s good enough for us too.

Tucking into a feast of juicy meats and steaming plates of vegetables, I decide Ilves might be on to something.

» Olde Hansa restaurant is just off the main square in Tallinn. See