I suppose it depends whose figure you want to cite. DW writes:
Poland is currently short of around 124,000 drivers, or 37% of its required workforce, according to a recent report by TI Insight.
Data from the UK's statistics office, the ONS, show the total number of truck drivers in the UK fell from 304,000 in the first quarter of 2020 to 235,000 in the second quarter of 2021, a net loss of 69,000. Logistics UK estimates the country is now approximately 90,000 drivers short.
It's a bit unclear to me if the two reports use the same methodology to derive those shortage figures though.
I've managed to locate that TI source. They indeed have Poland above the UK and the latter above Germany, but the estimates are at most for 2020.
Amusingly enough, Shapps has actually quoted those (TI) figures, only slightly off for Poland and choosing the top value for Germany... but he didn't seem to mention any concrete figure for the UK:
“We’ve got, for example, in Germany a 60,000 shortage and Poland a 123,000 shortage of lorry drivers, so as I say it is the principal cause of the problem and we are working very hard to change it, including changing the law in order to provide more tests for HGV drivers and encouraging people back into the market.
Politico put it in different (percentage) terms and from yet another data source:
The EU is grappling with a driver shortage of its own. The problem existed in both the U.K. and the EU even before the pandemic — in 2019 some 24 percent of trucker positions were unfilled in the U.K., while 22 percent were unfilled in Poland, according to the International Road Transport Organisation (IRU). In the Czech Republic, 21 percent were unfilled; in Spain, 20 percent.
There's a more recent IRU survey, which alas doesn't cover the UK. But looking at the latter survey, one has to be pretty careful at which point in time one makes the comparison, due to large variation in relation to the pandemic:
driver shortage was less serious in 2020 than 2019 due to the pandemic. In Europe, unfilled driver positions fell by around three quarters, from 20% to 5% for bus and coach drivers and from 24% to 7% for truck drivers.
Transport companies however forecast driver shortages to intensify again in 2021 as economies recover and demand for transport services increases. European companies are expecting a 17% shortfall in drivers this year. This shortfall is expected to reach 18% in Mexico, 20% in Turkey, 24% in Russia, and almost one third in Uzbekistan.
Finally, on the question whether the UK driver shortages were aggravated by Brexit, the BBC has this survey, posted on 27 September:
Brexit is given as a top reason in responses, together with drivers retiring.
The article also notes:
A Road Haulage Association (RHA) survey of its members estimates there is now a shortage of more than 100,000 qualified drivers in the UK. [...]
Even before Covid, the overall estimated shortage was about 60,000 drivers.
However, ONS data cited in The Grocer (on 19 Sep) seems to contradict that level of impact of Brexit, at least via EU drivers:
according to ONS data, the loss of EU drivers is only a minor cause of the shortage. At the start of 2020, before the pandemic hit, there were 37,000 EU drivers in the UK. Now, there are 24,500.
That loss of 12,500 drivers only goes a little way to explaining the current shortfall. Given a total of almost 70,000 HGV drivers left during the pandemic alone, this represents just 18% of those who exiting.
It led a logistics thinktank led by Driver Require to conclude “EU drivers leaving the UK did not significantly contribute to the current shortage”, in a new report published this week.
Still, this 18% is not 0%. And offering 5,000 visas to foreign drivers is an implicit admission that whatever streamlining of licensing/recruiting thanks to Brexit (as Shapps says happened) wasn't enough to fix the driver shortage, at least in the short term.
Unfortunately, it's difficult to say what demand changes occurred in the same time frame elsewhere in Europe as the data from TI for example is taken at different points in time and the IRU doesn't constantly survey the UK for some reason.
Regarding the UK fuel shortage, the immediate trigger appears to have been panic buying:
In the run-up to the fuel shortage, deliveries did fall in England although only marginally. At the start of September, fuel deliveries fell by around 200 litres per filling station on average.
This mismatch barely registers when comparing supply and demand earlier in the year, when far larger mismatches occurred.
However, as more people became aware of the shortage, panic-buying of fuel increased rapidly. Just several weeks after the initial fall in supply, sales of petrol skyrocketed.
According to the BBC, the sudden spike in demand appears to have been triggered by an announcement about driver shortages though, so the issues are related at least on that level:
On 23 September, BP warned it would have to "temporarily" close a handful of its petrol stations, because of a lack of drivers.
Long queues started to build up outside stations across Great Britain in the following days, amid fears that fuel might run out.
I haven't looked at the UK food issues in any great detail, but I recall reading some complicated stories about e.g. CO2 shortages affecting the packaging used in the industry. So shortages may have been due to Brexit in some way but not mediated by truck driver shortages. The same story mentioned lack of workers in meat production as a "result of labor shortages tied to Brexit and the pandemic", but not clear how much due which cause. (Besides driver visas, the UK government also announced 5,500 visas for poultry workers.)
I do see that some companies like McDonald's directly blamed the driver shortage as one of the factors for shortage of some of their products, like milk shakes, in the UK.