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Yes, you can do London on the cheap

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 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. No, 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. My friend Lindsay, a one-time exchange student at the London School of Economics, was visiting from San Francisco. 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. 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. 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.

On Sunday, 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 breakfast at the airport.