Alice-Azania Jarvis: It turns out London can be cheap and cheerful

London is expensive. Extortionately so – or so runs the conventional wisdom. And it's true: a pint in a Zone One pub costs considerably more than it does anywhere else. The tube is both a necessity and a luxury: yes, it gets you from A to B, but it's also pricey, crowded, dirty and unreliable. And that's before you even take into account the lack of large-scale supermarkets, shunned in favour of their more expensive "metro" equivalents. There's no doubting that London living isn't cheap. But what do visitors to the big city think?

Last weekend I got to see things from an outsider's perspective.

I viewed the rain with fresh disappointment. But the one thing I didn't find myself doing was despairing at the bill. The cost of living may be high, but if you look hard enough, there are plenty of bargains to be had in the city.

My friend Lindsay was visiting from San Francisco. A one-time exchange student at the London School of Economics, she is no stranger to London's sights and sounds. Still, it was her first visit for a few years and she wanted to make the most of it – without spending a fortune. And so I was tasked with devising an itinerary of the cheap and cheerful. And you know what, it wasn't as difficult as I thought.

First stop was Borough Market, an easy place to empty your wallet if ever there was one. Brimming with artisan cheese, pastry and chocolate, it's a maze of temptation. It's also a jolly good way to fill up for free. Most traders offer tasters – and much as they may complain about the freeloaders who pile in for bites of brownie or chorizo, they can't mind too much. After all, they're still at it, aren't they? A short walk away, the Tate Modern offered shelter from the rain and a bit of culture – without a single penny being spent. And the evening's entertainment? At £20, discounted tickets for a West End play were too good to turn down.

Sunday proved just as reasonable. A wander down Columbia Road, admiring the blooms and boutiques, offered amusement at no cost whatsoever. Brunch in Shoreditch got two meals for the price of one, and a walk on Hampstead Heath gave us the best views in the city – for naught. As Sunday night rolled around, with supper at my parents', Lindsay checked her wallet: £20 left over. Just enough for a coffee, a book and some breakfast at the airport.