He said that the doubling time for hospital cases was "around three weeks" and while the number of hospitalisations was "mercifully much lower", it was "not trivial".
I am afraid Whitty is not quoting the latest data. Hospital admissions are currently doubling every 15 days while beds occupied are doubling every 12 days. This is the result of the rapid growth of cases from the previous week. It is not the first time when twitter enthusiasts are looking at the latest data while government advisors are a few days behind.
However, there is also some good news. The growth of cases has been slowing down and the numbers are now doubling every 19 days (vs 9 days not too long ago). As we discussed, the trends also vary across local authorities. Some are on the way down, some are plateauing, others (e.g. South West) are increasing rapidly. It is not a homogenous picture. It looks like some period of rapid growth is unavoidable (regardless of vaccination levels) however areas with higher vaccination rates (e.g. South Tyneside) might be plateauing earlier than others (e.g. Blackburn).