The notion of right or left is rather fuzzy in practice. There's some truth in the statement that led to your question with respect to a few policy aspects; not so much with respect to others.
For instance, consider the UK's single payer health care system. The Conservatives know it is political suicide for them to seek to privatizing it. The US equivalent would be to have medicare for all in place, Republican grassroots fighting tooth and nail to keep it around, and Republican politicians campaigning to expand its budget.
Gun rights are another example. The UK is among the countries with the least gun circulation.
For the rest, the UK Conservatives are your typical conservative right-wing coalition outfit: pro big business, pro small government (in theory, at least), pro fiscal responsibility (also in theory, at least), pro limited immigration, with traditionalist tendencies, with fringe members exhibiting vague to blatant xenophobic tendencies, etc.
Labour's positions under Corbyn are clearcut populist left. Its policy positions are very close to those advocated by e.g. Alexandra Ocasio-Cortez in the US. Before Momentum activists took over, the coalition's leadership leaned more center-center-left, as in firmly centrist -- which prompted arch-libertarian Margaret Thatcher to quip that her greatest achievement was Tony Blair. A US equivalent to a UK Blairite might look somewhat like Pete Buttigieg.
The Lib Dems are pro-market centrists with vague libertarian tendencies. It's nothing like Ron Paul fundamentalists, mind you; just a run the mill keep businesses happy outfit, without the social conservatism that is often associated with it. (To answer a comment: see for instance how the Tea Party movement, which originally was a purely libertarian group, got overtaken by the Christian right a mere few weeks into its existence.) In a 19th century continental European setting, they'd almost certainly have been filed under liberals -- that is, pro-democracy and pro-bourgeoisie, but not progressives. I'd wager many US independents would identify with it.
The Brexit party is a single issue party. There isn't much to say about it besides that it is first and foremost about Nigel Farage, and that its MEPs (and supporters) include a hodgepodge of libertarian fundamentalists, xenophobes, and former communists. It's a bit hard to say what it stands for exactly. The US equivalent might look like the alt-right without the white supremacist connotations -- or put another way, disgruntled, disillusioned, and disenfranchised voters.
The Green party is, well, green. They don't really fit in the usual right/left spectrum, except perhaps somewhere to the left. There actually is a US Green Party which resembles them on most policy issues (it only has traction in California).
The various nationalist groups are a varied bunch. The Scotts and Welsh are centrists leaning left. The Irish range from center left to hard right insofar as I'm aware.