The viola da gamba, and specifically the viol consort, is certainly
more closely associated with England in the sixteenth and early
seventeenth century than the violin. By the early seventeenth
century, England seems to have already had a long tradition of consort
playing going back to the mid-sixteenth century. Since music
manuscripts from this period seldom indicate instrumentation, however,
there is some disagreement among historians over whether this music
was mainly intended for consorts of viols, or whether it might equally
well have been performed by consorts of wind instruments or even sung
without words. The most important genre from this time is the In
Nomine, whose significant composers include John Taverner,
Christopher Tye, William White and others. (If you have access to
JSTOR, you might be interested in an article on this subject by
Warwick Edwards entitled 'The Performance of Ensemble Music in
Elizabethan England', from which I have taken much of this
information.)
Interestingly, viol consort playing seems to have gone out of fashion
in the 1580s or 1590s, when Italian madrigals were more popular among
English musical amateurs. However, there was a revival of interest in
viol consorts in the early seventeenth century, when composers started
to take up old forms, including the In Nomine, which had been popular
fifty years earlier. John Coprario, Orlando Gibbons, and the later
works of William Byrd belong to this second generation of consort
composers. This music is more clearly intended for viols than the
sixteenth-century repertoire, since the ranges used often make it
impractical for wind instruments. Publications of vocal music from
this period also sometimes include the indication 'apt for viols or
voices' to indicate that they might be either sung or played by a
consort.
The violin was also making inroads into English musical life in the
early seventeenth century, but initially it was used for different
kinds of music, often music with a somewhat lower status than the
music played by viol consorts. Playford's Dancing Master is a good
example: the violin was considered to be an easy enough instrument for
a dance teacher -- someone not primarily a musician by profession --
to play tunes on for dancing lessons. (Caveat: I am less familiar
with the history of the violin, and I know that some writers assign it
a more prominent place in English musical history. E.g., there is a
book by Peter Holman entitled Four and twenty fiddlers: the violin at
the English court, 1540-1690, for example.)
In Italy at the same time, by contrast, the violin was being developed
into a solo virtuoso instrument by composers including Biagio Marini,
Marco Uccellini and others. To some extent, in England (and in France)
the bass viol continued to play the role taken by the violin in Italy,
as the virtuoso professional's solo instrument. The practice of
playing chordally on the viol (sometimes called 'lyra viol'), as
mentioned in another answer, seems to be an English development from
the early seventeenth century. Later in the century, from around the
same time as the Dancing Master there is a publication by
Christopher Simpson entitled The Division Viol, which is an
instruction manual for learning to improvise solo divisions on the
bass viol.
John Cooper or Coprario, as mentioned in Matthew Walton's answer, is an interesting example of an early
seventeenth-century English musician with one foot in the 'old' world
of the viol consort and the other in the 'new' world of the violin.
As well as fantasias for consorts from two to six viols, he also wrote
in the newer genre of the 'fantasia-suite' for violins, bass viol and
organ. These combine aspects of the old consort tradition with dance
styles, and arguably show an Italian influence in their sonata-like
instrumentation.
The English viol consort tradition continued in some form as late as
Henry Purcell's consort fantasias and In Nomines of c. 1680, but by
that time it was already considered old fashioned. The lutenist
Thomas Mace gave a famous description of the old tradition, and
complained about the new fashion for violins, in his Musick's
Monument of 1675:
[...] in my Younger Time, we had Musick most Excellently
Choice, and most Eminently Rare; both for Its Excellency in
Composition, Rare Fancy, and Sprightly Ayre; as also for Its
Proper, and Fit Performances [...] We had for our Grave Musick,
Fancies of 3, 4, 5 and 6 Parts to the Organ; Interpos'd (now
and then) with some Pavins, Allmaines, Solemn, and Sweet
Delightful Ayres; all which were (as it were) so many Pathettical
Stories, Rhetorical, and Sublime Discourses; Subtil, and Accute
Argumentations; so Suitable, and Agreeing to the Inward, Secret, and
Intellectual Faculties of the Soul and Mind; that to Set them forth
according to their True Praise, there are no Words Sufficient in
Language; [...] And These Things were Performed, upon so many
Equal, and Truly-Sciz'd Viols; and so Exactly Strung, Tun'd and
Play'd upon, as no one Part was any Impediment to the Other;
but still (as the Composition required) by Intervals, each Part
Amplified, and Heightened the Other; The Organ Evenly, Softly, and
Sweetly Acchording to All. [...] But now the Modes and
Fashions have cry'd These Things down, and set up a Great Idol
in their Room; observe with what a Wonderful Swiftness They now
run over their Brave New Ayres; and with what High-Priz'd Noise,
viz. 10, or 20 Violins, &c. as I said before, to a
Some-Single-Soul'd Ayre [...] (p. 233-236)
Mace is something of a cranky old man here -- he wrote his book when
he was already 60, and almost certainly going deaf, as well as saddened by the declining public importance of his own instrument, the lute -- but it still
shows something about the relative place of the viol and the violin in
seventeenth-century England, at least as seen by an old-fashioned musician.