The British-English adjective Tory-lite originated as a derogatory designation of New Labour.
—Collins English Dictionary defines the name New Labour as follows:

a rebranding of the British Labour Party and its policies undertaken by Tony Blair ¹ and his supporters in the run-up to the 1997 general election in the United Kingdom and maintained during the Labour Party’s period of government under Blair’s premiership. Never an official title, it denotes the more right-wing/social democratic trend in Labour thinking and policy intended to make the party electable after its electoral catastrophes of the 1980s.

¹ The British Labour statesman Tony Blair (Anthony Charles Lynton Blair – born 1953) served as Prime Minister of the United Kingdom from 1997 to 2007.

In the adjective Tory-lite:
– the name Tory designates the British Conservative Party;
– the adjective lite—phonetic respelling of the adjective light—designates a moderated version of something.

The adjective lite first appeared, with capital initial, as a commercial designation of a manufactured product that is lighter in weight, calorie content, etc., than the ordinary variety. It has been especially used of low-calorie beer.

And, indeed, the following title from The Independent (London, England) of Friday 24^th May 1996 associates Tory-lite (the initial letter L being capitalised) with two brand names, Flora Lite ² and Miller Lite ³:

Return of the light brigade
Now you can enjoy Miller Lite, Flora Lite, even Tory Lite. So why not British Music Lite? After all, it was once the Children’s Favourite. By Andrew Stewart

² Flora is the name of a brand of buttery spread.
³ Miller is the name of a brand of beer.

These are, in chronological order, the earliest occurrences of the adjective Tory-lite that I have found:

1-: From a letter to the Editor, published in The Guardian (London and Manchester, England) of Saturday 20^th May 1995—in which Tory-lite (conflated as one word, and the initial letter L being capitalised) jocularly occurs as a proprietary name registered and protected by law:
—Context: The author of this letter was reacting to the review by the British journalist Will Hutton (born 1950), published in The Guardian (London and Manchester, England) of Wednesday 17^th May 1995, of Making Welfare Work: Reconstructing Welfare for the Millennium (London: Institute of Community Studies, 1995), by Frank Field (born 1942), who was then a Labour Member of Parliament:

Will Hutton is not usually guilty of peddling the double-think of Tony Blair’s ToryLite™ party, but to call Frank Field’s notion of asking welfare recipients to draw up “career plans” a progressive one is like calling Michael Portillo ⁴ left of centre.
Kevin Gopal.
42 Claridge Road,
Manchester M21 1WG.

⁴ Michael Portillo (born 1953) was then a British Conservative Member of Parliament.

2-: From the column Viewpoint, by George Anderson, published in the Evening Express (Aberdeen, Aberdeenshire, Scotland) of Friday 16^th June 1995:

Tony Blair, leader of the new Tory Lite party, would just grin, grin, grin.

3-: From the column Westminster, by Simon Hoggart, published in The Sunday Tribune (Dublin, County Dublin, Ireland) of Sunday 15^th October 1995:

The Conservatives are testing numerous methods of salvaging the election. Like a hypochondriac emptying the pharmacy shelves, they will try almost anything. Often these are mutually contradictory: on the one hand, they say, the Labour Party has either adopted, or tacitly agreed to, most Tory policies. Why, they ask, go for the cheap, imitation Tory lite party when you can have the real thing?
On the other hand, they claim, Labour has not really changed at all. The moment they return to office the currency will collapse, strikes will bring the nation grinding to a halt and taxpayers’ money will fund self-esteem workshops for handicapped lesbians across the land.

The adjective Tory-lite has come to be applied to a supporter of the policies of New Labour—as in the following from MG Rover? Same as New Labour, by Alexei Sayle, published in The Independent (London, England) of Tuesday 12^th April 2005:

Some people said in the honeymoon period that Blair and Brown ⁵ were just acting like Tories-lite so that they could get elected, then afterwards would reveal themselves in their true socialist colours.

⁵ The British Labour statesman Gordon Brown (born 1951) served as Prime Minister of the United Kingdom from 2007 to 2010.

The adjective has occasionally been spelt Tory-light—as in the following from A new wealth-creating agenda for the Labour Party, by Mariana Mazzucato ⁶, published in The Guardian (London and Manchester, England) of Monday 15^th January 2015:

A consensus is developing about why the Labour party lost—and lost big time—in the UK election. But the consensus is wrong. To those relying on the polls for prediction, the result came as a surprise. But for those who have followed Labour in the last years, have tried to influence their policies and have been frustrated by the lack of a seriously different story—on what caused the crisis, what to do during it and how to get out of it—it was less surprising.
In many ways, what Labour offered was ‘Tory Light’: ‘We too will cut the deficit, but less’. ‘We too think immigration is a problem, and will aim to let fewer immigrants enter, but more than the Tories’. In other words, there was no serious effort to develop a story on why running a deficit now could hold the key to future growth. (Look at the US, that ran a 10% deficit in 2009, and is today growing more than any European country that has been running a surplus). And there was no serious story on why immigration has actually been one of the key strengths of the UK economy, both in terms of the human capital it has attracted and the way this has resulted in a less provincial island mentality.

⁶ Mariana Mazzucato (born 1968) is a professor of economics at University College, London.