"quite high levels" is correct and can be used in written English.
For example, "The results from the experiment showed quite high levels of contamination."
"The UK is not alone in experiencing quite high levels of immigration".
"I sat in the gondola last night with him, it's an incredibly complex piece of machinery... He's also prepared to take quite high levels of risk".
It published a response in which it claimed that its findings "have shown convincingly that the seabed and its inhabitants can sustain quite high levels of fishing activity before negative effects occur".
A mild winter means that Europeans have currently quite high levels of gas in storage; it is also spring and, as Arthur Scargill discovered when he called a miners' strike in March 1984, that is not the best time to exploit producer power.
"This flagged up that these sort of farming initiatives are still being considered at quite high levels," he explained.
"I've worked in business at quite high levels so I hope it's not that much of an issue.
It also criticised what it described as the "quite high level" of spending on business lunches.
The most dangerous condition on the freeway is that there exists a medium traffic flow while vehicle speed keeps at a quite high level.
"The discussions we've had at the moment are quite high level, we haven't moved onto the financial numbers as of yet.
"But… telling Facebook explicitly what your line in the sand is on different categories of content is in itself giving Facebook a whole lot of quite high level information that they can use for profiling again.
The separation of the total resistance of the cell in its ohmic and polarization components allows the film electrolyte conductivity to be calculated, which attains quite high level (2.4 and 3.8 mS cm−1, respectively).
