is it likely that my US-issued card will be generally usable in the UK
and other countries with the chip-and-pin system, or should I be ready
to exchange cash?
You should be able to use your card at most places, in the UK and other countries too. At least ATMs and most shops accept it, while some vending machines may require a chip-and-pin (i.e. EMV) card.
Wikipedia has this to say (regarding UK & Ireland):
While most terminals will still accept a magnetic strip card, and the
major credit card brands require vendors to accept them, poorly
trained staff may refuse to take the card under the mistaken belief
that they will be held liable for any fraud if the card cannot verify
a PIN. Non-chip-and-PIN cards may also not work in some unattended
vending machines at, for example, transport stations.
If you're still worried, there are options like this:
In 2010 a
number of companies began issuing pre-paid debit cards that
incorporate the Chip & PIN which allows Americans to load up cash as
Euros or British Pounds.
In Finland, ATMs have two slots: blue for chip cards and yellow for legacy cards with only magnetic stripe. (In most counties using EMV there's just one slot for both kinds of cards though, AFAIK.)
Photo credit: Etelä-Suomen Sanomat