Yes this is true, although most jurisdictions impose fairly low upper limits on the amount of consideration that a verbal contract can cover. As of 2012 the most common value was $500 or less (and probably is still the same level or close to it in most areas). Anything involving consideration valued at more than $500 USD was not binding unless written.
Furthermore, contracts can be implied. IANAL, and I can't quote the UK case, but IIRC correctly it boils to whether there was "an intent to create legal relationships". The case involved a lottery pool in which the pool won. There was one named winner, and he decided not to pay out the winnings to the other participants. The other participants sued to obtain their share of the payout, naturally. They won the case because although no verbal agreement was made, there was an implied legal contract.