Brexit is a factor especially in sectors where we've spent years propping ourselves up on cheap, mobile labour or internationally trained graduates.
Our problems run deeper than that. Education is not aligned to future employment needs, e.g. NHS medical staff, paying bursaries to encourage people through long courses with anti-social hours. Gove set the education system on a narrow cheap academic pathway and dropped the vocational courses that fed into the trades.
Many shortage/ retention issues are about excessive paperwork that clog up productivity. It can take months to replace staff leaving gaps where a backlog builds up that never shifts. People are driven out of jobs that have become about accountability and demonstrating political targets, not delivering the core service.
The roots of a lot of this go back into the New Labour days, but grossly exagerated since 2010. Also since 2010 austerity has reduced public funding to a skeleton service with no flexibility to accomodate disruption.
The other (global) issue that's not been mentioned is the supply chain disruption from continued lockdowns in China. This year I've been talking to the guy in the furniture shop and independent shoe shop and both have the same issue of irregular supplies of basic components being made in China, springs, buckles and this messes up all the rest of the production chain and puts up costs.
While the Ukraine/ Russia situation is affecting grain prices, again China has disrupted its agricultural production by people not being allowed out to farm the land and missing production stages, plus distribution areas as truck drivers can end up either not being allowed in to lockdown areas and having to dump and waste produce, or being allowed in but then being detained/ locked down. This increases demand on grain supplies. Added to that again there have also been poor harvests in other grain producing areas.
Brexit is a complication and it will take time (years) for economic forces to balance out, and awkwardly it's hard to assess the actual impact at a time following 2 years of pandemic response disruption and war. The UK is not unique in having a rough phase though.