If you asked the Sage of Ely whether free movement of labour reduced wages you would be told not to be so silly. If you insisted that immigration might, under certain circumstances, be the reason for low UK wages you’d be called a racist fascist:
What there is, yet again, is a breakdown in the supply chain due to a shortage of lorry drivers. And the reason why there is a shortage of lorry drivers is that Brexit and government intransigence has tipped what was already a delicate labour market into crisis.
There is no short term resolution to that crisis. The UK government has decided to alienate and even expel a significant part of a labour force on which the country has relied and has, despite warning being given, chosen to do nothing to ameliorate the situation until it is now too late for anything it might do to relieve that labour shortage. So, like it or not, we do not have the drivers that we need, and nothing can now be done about it.
The absence of free movement of labour increasing wages is not proof that you’re not a racist fascist.