I do not seriously think restaurants that have spent years building a recognised brand are going to rely on home cooking to deal with demand they cannot fill.
Restaurants will not suffer any more than the other industries that rely on low paid workers to make their profits.
A lot of food retailers use people from non-EU countries already,for example overseas students working part time while studying and short term workers on temporary Visas.
If these positions cannot be filled there will have to be wage increases which will result in higher food bills but may go to address the imbalance between low paid workers and those in white and blue collar jobs.