The phrase "despite liking" is correct and usable in written English.
You can use it to introduce a contrasting idea, e.g. "Despite liking the restaurant, I decided to try a different place next time."
And for some reason, despite liking Made In Chelsea and Towie, I'm not a fan of Geordie Shore.
Congratulations to the many pro-European Tories who voted against Zac Goldsmith, despite liking him as a person.
Mind you, I complain about art fairs despite liking them quite a bit, especially if I don't have to leave town to see them.
Robert Rodriguez was offered the chance to direct, but turned down the offer due to his commitment on The Faculty, despite liking Smith's script.
Despite liking actor Lance Reddick, Wigler was displeased with his character's increased screentime, believing Broyles works better as an "enigmatic figure".
Despite liking the fact that Scully was the focus of the episode and praising Anderson's performance, he thought that its "main flaw" was the way it handled her moral crisis, opining that she appeared too weak.
Despite not liking the term, Ben Van Praagh begrudgingly admits he is a serial entrepreneur.
Despite really liking Sailfish, I was ultimately unable to use the operating system for my experiment.
Yet he uses three words in the article that I did not know despite, like him, being a former scholar of Brasenose College, Oxford.
Will Hughes 6 Started against Sweden and was neat enough despite, like all his central midfield colleagues, struggling to impose himself forcefully on the game.
Fanning said that despite "Like a Dog" being about a political issue, it was not a political song, rather just Powderfinger "voicing our opinions".
