In America, the word "Formica" refers to the laminate wood surface of a certain era.
Not quite. It refers to a laminate material of a particular composition; cardboard or paper (once also fabrics) and melamine. It's more melamine than anything else, but often given a faux-wood finish. (Sometimes a faux-stone or plain finish is preferred).
Melamine is the plastic of "unbreakable plates", which while not quite unbreakable (I found out the hard way that my skull is in fact tougher than such a plate) are hard-wearing and heat-resistant (but do not microwave the stuff, I found that out the hard way too). It was once quite fashionable for dinnerware, but now mostly used for camping or children's dinnerware only, where the hard-to-break quality is particularly useful.
Formica® is a registered trademark of the Formica group, and comes from it being used in rôles where people were often using mica; hence it is used "for mica".
It's had a bit of the genericised trademark effect, in that people will use the word to refer to similar laminates too, as well as for Formica®.
(Correct me if I'm wrong on this, as I'm not an American.)
While originally developed in the US (the first customer was the US military), the Formica Group are based in New Zealand, and manufacture the material in the UK, Mexico, Canada, Thailand, Taiwan, and other countries.
It is used there, and more widely, and similar laminates are made more widely still.
This word has a certain retro feel to it.
The sort of coinage that gave us "for mica" → Formica® would not be as likely today, nor would it have been as likely much more than a century before then. The word is very much of its time.
So it would not be used for today's laminated wood.
While the word is a bit dated, the material is still in considerable use.
I last bought some Formica® counter tops for a kitchen in 2011. Better than any wood in terms of resistance to blades and heat, and granite or marble is outside of my budget (and in fact Formica® is less likely to chip than they are).
Is this word also used in Britain in the same way?
Yes, and Ireland, Canada, New Zealand and Australia.
In most other languages that use the Latin script it is still formica or undergoes just a little change (in Spanish it is fórmica). In other scripts it tends to just be transliterated to فورمايكا, 福米卡 or other things that still sound close enough to the English word. In Finnish it can be either formica or the more general muovilaminaatti ("plastic laminate").