In a new study bbc.co.uk/news/amp/health-5... only 13 percent of blood cancer patients had an antibody response three weeks after their first dose of the Pfizer vaccine, falling to only 8 percent after five weeks. The response rate for patients with solid cancers was initially three times higher and did not fall after five weeks.
Those cancer patients given a second dose just three weeks after the first had a much higher response. This could persuade the UK government to bring forward the second vaccination for cancer patients (the current interval is twelve weeks).
This is a small study, Pfizer vaccine only, and we need more information, but for now CLL patients whether vaccinated or not remain at high risk.
Addendum: here are some expert comments on the preprint article (not peer reviewed) about this study