The term Tory is synonymous with the Conservative party. It is not a very flattering name, it is associated with aloof elites. I think left leaning Brits probably use the name "Tories" much more than "Conservatives".

https://en.wikipedia.org/wiki/Tories_(British_political_party)

from wiki

Conservative Party The Tories became associated with repression of popular discontent after 1815, but the Tories later underwent a fundamental transformation under the influence of Robert Peel, who was an industrialist rather than a landowner. Peel in his 1834 Tamworth Manifesto outlined a new conservative philosophy of reforming ills while conserving the good. The subsequent Peel administrations have been labelled Conservative rather than Tory, but the older term remains in use.

When the Conservative Party split in 1846 on the issue of free trade, the protectionist wing of the party rejected the Conservative label. They preferred to be known as Protectionists or even to revive the older Tory as an official name. By 1859 the Peelites (Peel's Conservative supporters) joined the Whigs and Radicals to form the Liberal Party. The remaining Tories, under the leadership of the Earl of Derby (a former Whig) and Disraeli (once a Radical candidate for Parliament), adopted the Conservative label as the official name of their party.