The only possible link I can think of between Brexit and the small boats is that it's known that the people smugglers previously made use of the trucks going from France to the UK. Increased checks on imports and exports since Brexit may make it more likely for them to be found, so they've turned to the boats instead.
It's perfectly possible that the only change is that illegal immigration was always going on but has become much more visible as a result of Brexit.
There are still other invisible routes too, e.g. EU to Ireland, catch a bus to Northern Ireland then get the ferry to GB. Usually no passport or ID needed at any point. Join the vast UK black market for work, much more easily and safely and this won't feature in any statistics.