If I had an OED, I could be more specific, but the phrase rat-run is in the Oxford Online Dictionary:

British informal A minor, typically residential street used by drivers during peak periods to avoid congestion on main roads: 'our road was used as a rat run between two main roads.'

Etymonline lists rat-run from 1870 "in a literal sense", but doesn't give an example of its use other than a mention next to rat race.

An Asperger Dictionary of Everyday Expressions written in 2004 gives the definition (as does The Oxford Dictionary of Phrase and Fable of 2006):

A faster route between two points that is circuitous but avoids traffic hold-ups.*

The * denotes a level of impoliteness (I have no idea about the title!)

Finally, and interestingly, rat run is defined in the Spanish, but not the English) Collins:

rat run (Brit) (Aut) calle residencial usada por los conductores para evitar atascos (a residential street user by drivers to evade traffic jams.)

So, it's not a short cut by distance but is by time, and it seems to be better known in Britain than in the US.

_{I can easily imagine this coming from rat behavior in mazes. A-mazing research, Dr. C. James Goodwin writes (on the importance of rat maze studies:}

_{In his 1937 APA presidential address, the noted neobehaviorist Edward Chace Tolman, PhD, made a startling claim: "Everything important in psychology … can be investigated in essence through the continued experimental and theoretical analysis of the determinants of rat behavior at a choice-point in a maze."}

_{This venerable tradition might well have it's origin in the Hampton Court Maze built in 1690 just outside London. The first maze study was conducted Willard Small and Linus Klineby (who had just returned from a visit to London in 1890s),two graduate students in psychology. Their 6' x 8' maze was called "the Hampton Court Maze".}

You take a rat run usually to avoid traffic and spare time.

Rat run [countable] British English: (from Longman dict.)

• a quiet street that drivers use as a quick way of getting to a place, rather than using a main road:

  • The road has become a rat run for traffic avoiding the town centre.

Rat run: (from www.thorne_slang.enacademic.com)

• (British) a side street used for fast commuter traffic. A phrase and phenomenon of the late 1980s.

The following article is from a Taxi Magazine: (from www.pubcat.co)

• Why do we keep hearing about certain roads being used as a “rat run”? It sounds horrible doesn’t it? We read it in the paper, or hear it on local radio; and duly recoil at the image of dirty rodents running through slimy sewers and up greasy drainpipes. The media have done their job: they have made a traffic cut-through seem dirty and wrong. Those who dare to think their way around alternative streets in order to avoid congestion are likened to rats, and are seen as negative and anti-social.

As suggested by some users, the expression is used also in Australia: (from The West Australian)

• Rat runs raise safety fears on back streets Perth's growing traffic congestion has spilled over into small suburban streets as motorists search out peak-hour shortcuts known as "rat runs".

• Rat runs have sprung up all over the metropolitan area, putting pressure on streets that were not built to handle large volumes of traffic.

Considering the above, the expression appears to have a recent coinage ( late 80's); your British friends would probably understand its meaning ( traffic issues are very popular); and it is used also in Australia. The reference to rats running through sewers and drainpipes to move quickly through places ( as suggested in the taxi magazine article) is very suggestive..and probably a reliable one. –

A 'rat run' is a term very widely used in Britain, particularly in South-East England which has some of the world's most congested road traffic.

At busy times you have an advantage if you know 'the rat runs' i.e. the minor residential streets which get you past bottlenecks etc.

But, in response to appeals from residents, a lot of local authorities have either blocked them off with bollards part way along, or put in traffic calming measures such as humps or chicanes where vehicles going in opposite directions cannot pass.

Is a rat run similar to taking a shortcut?

Not really. Quite simply, it is a minor street (let's say: "not supposed, by the authorities, to be used by commuter traffic") that is cleverly / sneakily / craftily / ironically used to avoid being on the "normal" major traffic streets. It would usually be shorter, but may be more circuitous as it avoids traffic.

As John Mee and Erik Kowal have both pointed out, it is a noun.

Josh61 has already posted the correct definition "rat-run: (British) a side street used for fast commuter traffic. A phrase and phenomenon of the late 1980s. link" Another correct definition from the OED, courtesy of Medica "British. informal. A minor, typically residential street used by drivers during peak periods to avoid congestion on main roads: 'our road was used as a rat run between two main roads.'"

How well known is it?

Every person in Britain, especially Londoners, know it.

Note too that the meaning is obvious, rats tend to scurry down pipes, tiny lanes, and gutters in order to avoid populated areas

I have to admit I love it!

It's an exceedingly rich expression so you are very wise to love it. You know how the single worst thing, in the Universe - worse than Nazis, worse than vegetarianism, worse than 5th degree burns, worse than child molestation, worse than politicians, worse than terminal cancer - is Commuting. It rather makes you think of the phrase...

The rat race

and just how the whole situation is unbearably horrible. Traffic in London is a killer: somehow rat run manages to do a number of things at once:

(*) It is rather derogatory towards the "civilians" living on the nice little quiet residential streets. ("Screw those rich bastards with their Balthaup kitchens - to me it's just an ugly pipe like a damned rat would run down. I'll drive on it if I want to! Hah hah! Keep your damned kids inside!")

(*) It anti-enobles the whole entire act - the whole lifestyle - paradigm - milieu - of living and working in London, down to a pointless, animalistic, disease-ridden subconscious scampering: in filth.

(*) For me it really captures the 80s (for some reason it's really like a kind of Brit equivalent to the film "Wall St", you know?): it has a pithy, brutal, self-aware-of-greed-and-pointlessness quality. Quite amazing.

For me personally, it immediately connects with The Stainless Steel Rat dystopian novel by Harry Harrison— commuters in a small way trying to beat the system; hopeless of course, but then we're all just... rats.

Note that as with any issue in the UK, it immediately became a sort of central issue in the overall police-state, authoritarianism, general sort of ongoing social battle. "The man" immediately tried to clamp down on drivers using rat runs, via adding strange bumps on the roads and so on. (In contrast, government-sponsored public transport vehicles such as buses got their own lanes. "Oh, you wanna try using rat runs huh? How's THIS? Stfu and pay taxes" ... sort of thing.)

Here's a poor attempt at indicating a typical London rat-run, but I encourage any real Londoners to click Edit and put in a better one (using AZ rather than the non-British Google.maps!) I wonder if any black cab drivers use this site as a pastime?

Poor example of a rat run. You avoid a very busy intersection by nipping along some residential streets, making as much engine noise as possible to irritate the overseas wealthy.