With the British pound struggling against the U.S. dollar, now is the time for penny pinchers to head across the pond. If you're looking for an afternoon of cheap thrills in London, it’s as easy as a walk in the park … or, rather, beside the river.

As I’ve discovered while entertaining visitors in the city I’ve called home for more than a decade, one of the best (and most affordable) ways to acquaint yourself with the U.K. capital's iconic sites is by pounding the pavement along the Thames. With this 3.5-mile-long, self-guided walking tour, you can experience 1,000 years of history, without the aid of Dr. Who’s TARDIS. You might opt to spring for admission to some of the sterling attractions along the way, but you aren’t obliged to burn a lot of cash … just calories.

Start the day with iconic views of Westminster Abbey, the Houses of Parliament and Big Ben, all clustered a few minutes from the riverbank. Of course, Big Ben is really just the name of the clock’s bell, which will remain silent until renovation works are completed in 2021. The tower itself was officially christened Elizabeth Tower for the Queen’s Jubilee in 2012, but nobody calls it Big Bess, which might not be construed as the most flattering term. Granted, the royals haven’t beheaded anyone in rather a long time, but why tempt fate — or the Queen?

After synchronizing your watch to Big Ben, which marked 160 years in situ this July, cross Westminster Bridge to the south bank. Here, you may be tempted to shell out for a spin on the London Eye. As one of the tallest Ferris wheels in the world, it offers spectacular views on a clear day. You’ll be encased in a large capsule, so even if you’re afraid of heights you might be able to stomach the ride without tossing your cookies — or scones, as the case may be.

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Thrill-seekers might also consider a round-trip speedboat tour of the Thames with London Rib Voyages, which departs near the London Eye. Just be sure to book ahead — and bring a sturdy comb. You’ll feel like a Bond babe whizzing up the river in the wake of some imaginary villain, but barring the emergency intercession of a skilled hairstylist, you’ll look like Medusa by the time you disembark.

From the Eye, head east. Stick close to the river as you make your way toward your ultimate goal, the Tower of London, with plenty to see along the way.

On the riverside path, you’ll often find street performers kitted out as anyone and everyone, from Captain Jack Sparrow to Elvis. So consider this a cheap and cheerful substitute for Madame Tussauds.

Keep your eyes peeled for the Tate Modern on your right. It recently overtook the British Museum to become the most popular visitor attraction in the U.K., and there is no charge to visit. If you consider displays like Damien Hirst’s formaldehyde-encased shark, which was on show here in 2012, to be 21st-century masterpieces, it’s a must-see.

From here, it’s just a stone’s throw to Shakespeare’s Globe. It’s not the original theater, which was destroyed in the 17th century, but a thatched-roof reconstruction that opened in 1997. You’ll have to loosen your purse strings to take a tour or watch a play, but hey, selfies outside are free.

Cast your eyes across the river for a view of St. Paul’s Cathedral before carrying on toward a full-sized replica of the Golden Hinde, the 16th-century English galleon in which Sir Francis Drake circumnavigated the globe. For a few quid, you can take a guided tour of the ship to experience what life was like onboard more than 400 years ago. (Spoiler alert: There were no casinos or midnight buffets.)

Sadly, the "new," although not necessarily improved, Golden Hinde has abandoned the old British naval tradition of dispensing grog. So if you want to wet your whistle or indulge in some nibbles, reserve a table for lunch or afternoon tea (or perhaps something stronger) at the Shangri-La hotel at the Shard, a neck-craning inverted icicle of a skyscraper — the tallest in Western Europe — that also offers a pay-per-view panorama of the city from 800 feet high in the sky.

Having satiated your cravings, head north back to the Thames, where you have the option of a tour aboard the World War II-era HMS Belfast ship museum. If that doesn’t float your boat, skip it and continue east towards Tower Bridge.

Now, you could simply stroll across the bridge for free. However, you'll have to prise open your purse if you want to visit the Tower Bridge Exhibition, which explains the history and construction of this impressive span, with a gulp-inducing galumph over a glass floor walkway 42 meters above the Thames.

Once you’ve crossed to the north bank, you’re just steps from your final destination: the Tower of London, a huge walled complex with the turreted White Tower built by William the Conqueror at its center. If you stand outside the walls at the northeast corner and look southwest, you can glimpse a millennium of architectural evolution, with the Shard appearing to rise up out of the ancient fortress like a futuristic mother-in-law suite — evidence that city planners might have a sense of humor after all.

Not even condemned criminals are allowed “free entry” to the Tower of London anymore. But once inside, take advantage of the complimentary hourlong tours offered by the beefeaters, who are typically as funny as they are informative. You could easily spend an entire day here, gawping at the crown jewels, walking the ramparts and examining centuries-old weaponry, armor and (yikes) instruments of torture.

Be sure to explore Beauchamp Tower, too, which is located within the complex next to the chapel where Henry VIII’s beheaded wives are buried. From a tiny room on the second floor of Beauchamp, you can peer out a window at the green where many unfortunate “residents” of the tower met their gory fate.

The prayers, poems, fears and sorrows of the condemned are etched into the walls all around you. These folks didn’t just scrawl a bit of graffiti. They chiseled their missives into the stone, ensuring their entreaties for mercy would never be forgotten.

Granted, it could make for a sobering end to your day. My advice? Head to the nearest pub and drink a toast to the fallen. Of course, there are a lot of fallen to drink to, so be careful you don’t trip and fall yourself on the way out.