There's an absolutely fascinating history of independent taxation in the UK in this 1995 House of Commons research paper "Tax and Marriage". Some choice extracts below.
Certainly income tax in the UK used to be paid as a couple originally:
Since the introduction of income tax in this country in 1799
... a married woman's income has
been taken to be but part of her husband's, and taxed accordingly. The
Income Tax Act 1806 directed that any profits earned by a married
woman "shall be deemed to be the profits of the husband."
and that was pretty much the status-quo for almost two centuries:
The language
used in section 279 of the Income and Corporation Taxes Act (ICTA)
1988, which codified this rule prior to the introduction of
independent taxation, shows little change over the intervening years:
"A woman's income chargeable to income tax shall ... during which
[time] she is a married woman living with her husband, be deemed for
income tax purposes to be his income and not her income."
Although the rules did change over the period:
A number of
changes were made during this century mitigating the inequalities of
this rule, three of particular importance.
In 1918 an additional tax
allowance was introduced - the so- called "wife" allowance - given to
all married men; this was the first specific provision made by the
income tax system for married couples. At the time, it was felt that
recognition should be given to the additional financial burdens that
marriage imposed. One usual consequence of a wedding was that two
people became dependent on the one (husband's) salary, while sole
responsibility for the care of children usually fell to a wife.
From 1914 spouses could elect to file their own tax return, being
liable to pay tax on their own income. However this election had no
effect on their aggregate tax liability. The two incomes were added
together, tax due on the joint income was computed as if the joint
income was the husband's, and the tax liability was then apportioned
between the spouses roughly in the ratio of their incomes. The system
was complicated and unpopular, both with taxpayers and the Revenue.
In 1971 an election for separate taxation of a wife's earnings was
introduced. Couples could elect to have their earned income assessed
separately for tax, and a wife's earned income was taxed as if she
were a single person. This election had to be made jointly, and any
unearned income enjoyed by a wife continued to be aggregated with her
husband's when assessed for tax. Although the wife claimed her own
single person's allowance, neither spouse could claim either of the
married allowances. Election for separate assessment was only
attractive for couples with relatively high incomes, where the wife
had significant earned income.
...
Despite these changes, the fact
remained that on marriage a woman lost her rights to financial privacy
and independence.
Pressure for independent taxation grew:
Despite the introduction of the wife's earning election in 1971,
aggregation of spousal income came in for increasing criticism during
that decade. An indication of the pervasive nature of the system was
given when finally, in 1978, the Inland Revenue changed its practice
of replying to any correspondence from married women by simply writing
to their husbands.
Instead, tax offices were instructed to write directly to the person
concerned.
That same year, 1978, the Equal Opportunities Commission
published a highly critical report on the taxation of married couples.
The Commission argued that individuals who did the same work should
expect to receive the same reward and be taxed on that reward in a
like manner. Indeed, the taxation of men and women as individuals,
irrespective of their married status, was the only approach consistent
with the Sex Discrimination Act 1975 and the Equal Pay Act 1970 .
The document describes a lot of wrangling over the details of reform, particularly around the transferability of unused allowance. But eventually:
Determined to have a scheme up and running before the next election,
Nigel Lawson developed what was, in his own words, a 'half-way house',
which he announced in the 1988 Budget. From the start of the 1990-91
tax year, a husband and wife would be taxed independently on income of
all kinds.
...
Chancellor Nigel Lawson, said in his 1988 Budget speech when first
announcing its [independent taxation's] introduction, "the present
system ... takes the income of a married woman as if it belonged to
her husband. Quite simply, that is no longer acceptable."
And here we are, although of course there has been much subsequent tweaking, in particular the rapid elimination of "Married Couple's Allowance" which was introduced with the reforms and intended to reduce the impact on couples who had benefited from the old approach (see comment below this answer and pages ~16 in the linked PDF).
The token "Marriage Allowance" introduced 2015 and described in Tom Revell's answer seems to me to been a political stunt borne out of some sort of nostalgia for the Good Old Days of joint tax returns and transferable allowances. The IFS commented on this when it was announced in 2013:
As the maximum gain is less than £4 per couple per week, effects on
incomes and incentives would be small.
The social message sent by the tax break looks more significant than
its financial consequences for families, as the Prime Minister has
stated himself. But as a structural change to the tax system it may
ultimately turn out to be more important. First, it would re-introduce
an incentive to marry in the income tax system, just when Married
Couples’ Allowance - now available only where one spouse was born
before 6 April 1935 - had been almost entirely phased out.
...
Second, the transferral of allowances between spouses would
re-introduce an element of joint income taxation. This is inescapable
if the aim is to assess people based on family characteristics (in
this case, to target single-income families) as our benefits system
already does, rather than based only on individual characteristics.
There is a much wider, principled debate behind all this about the
role of joint versus individual assessment.
Perhaps one day we will find we have gone full-circle?
