People are available, if the salaries are there. Part of moving away from neo-liberalism is to stop the endless race to the bottom. If the pay and conditions of lorry driving become better than being a Happiness Engineer at Kidderminster District Council, that's where you get your staff from.
Immigration to supply labour is always a ponzi scheme. If you have a closed system though, you can rebalance and see the most valuable jobs rewarded. Reducing overall consumption and moving to localise supply chains also needs to be part of this rebalancing.
I always saw curbing population growth, and hence improving wages, as part of Brexit.
Btw I absolutely support immigration for social reasons (love, asylum and study), just not economic immigration (exploitation of the most vulnerable in both the exporting and importing countries by the most powerful).